Basics of digital circuit engineering. Under the elementary conjunction of logical functions, the l Ogatic product of all the arguments of the function taken once with a sign or a sign of inversion

The study of digital circuitry should be started with the theory of automata. In this article you can find some elementary things that will help not get lost in further articles. I tried to make an article easily and confident that an unprepared reader would be able to easily figure it out.

Signal - Material information media used to transmit communication communication messages. The signal, in contrast to the message, may be generated, but its acceptance is not required (the message must be taken by the receiving party, otherwise it is not a message, but only a signal).

The article discusses a digital discrete signal. This is such a signal that has several levels. It is obvious that the binary signal has two levels - and they are taken in 0 and 1. When the high level is indicated by one, and the low zero is called a positive one, otherwise negative.

The digital signal can be represented as a temporary diagram.

There are no discrete signals in nature, they are replaced by analog. Analog signal cannot move from 0 to 1 instantly, this signal has a front and a cut.
If you draw simplifier, it looks like this:

1 - Low signal level, 2 - high signal level, 3 - signal growth (front), 4 - Signal recession (slice)

Signals can be converted. To do this, logical elements are used in practice, and logical functions are used formally. Here are the main:

Negance - inverts the signal.
The schemes are indicated as follows:

Logical or (logical addition, disjunction)

In the scheme:

Logical and (logical multiplication, conjunction)

In the scheme:

The last two may have denial of the output (and non-or-no). The values \u200b\u200bof their logical functions are inverted, and the output is drawn in the circuit.

The summary table of the logical functions of two arguments looks like this:

Working with logical functions is based on the laws of the logic algebra, the basics of which are set forth in the attached file. There are also tasks for self-control and test questions on the topic.

Design of logic schemes using the functions of the logic algebra

Schemes of the first kind. combination circuits, the output signal of which depends only on the state of the input signals at each time of time;

Schemes of the second kind or accumulating schemes(schemes sequence) containing accumulating circuits ( elements with memory), the output signal of which depends on both the input signals and on the state of the schema in the previous points in time.

By the number of inputs and outputs, there are: with one input and one output, with several inputs and one output, with one input and multiple outputs, with multiple inputs and outputs.

According to the method of implementing the synchronization of the scheme there are With external synchronization (synchronous automata), with internal synchronization(Asynchronous automata are their special case).

Almost any computer consists of a combination of schemes of the first and second kind of different complexity. Thus, the basis of any digital machine processing digital information is the electronic elements of two types: brain teaser or combinational and memorable. Logical elements perform the simplest logical operations on digital information, and storage serve to store it. As you know, the logical operation is converted by defined input digital information rules on the output.

It can be assumed that the elementary logic functions are logical operators of the electronic elements mentioned, i.e. schemes. Each such scheme is indicated by a specific graphic symbol. (They were presented above - elements and, or, not, or not, and no)

An electrical functional logic converter (combination machine) that implements the logical function is presented as an example below. In the element base from the logical elements and, or, not.

For consolidation, I propose, independently synthesize the logical scheme that implements the following logical functions:

You can do this for example in Electronic Workbench.

Here for example, the first completed task:

Your journey into the world of electronics We will start with immersion in digital electronics. First, because this is the top of the pyramid of the electronic world, and secondly, the basic concepts of digital electronics are simple and understandable.

Did you think about what a phenomenal breakthrough in science and technology occurred due to electronics and digital electronics in particular? If not, then take your smartphone and look attentively on it. Such simple design is the result of the huge work and the phenomenal achievements of modern electronics. Creating such equipment was made possible by a simple idea that any information can be represented in the form of numbers. Thus, no matter what information the device works, deep inside it is engaged in treating numbers.

You certainly are familiar with Roman and Arabic numbers. In the Roman system, the number is presented in the form of a combination of letters I, V, X, L, C, D, M, and in Arabic using a combination of characters 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9. But there are other forms of the number of numbers. One of them is a binary form. Or, as it is more common, a binary number system. In such a number system, any number is a sequence of only "0" and "1".

Mathematics with engineers worked well, and today any information can be presented in the form of a combination of zeros and units: a signal from the motion sensor, music, video, photo, temperature, and even this text that you now read, in fact in your depths The devices have a form of a sequence of zeros and units.

Regardless of which information is operating a digital device, deep inside it is engaged in treating numbers.

Why exactly "0" and "1", and not "0", "1" and "2", for example? In fact, there were quite successful attempts to create a digital technique, which uses not binary, and the Tropic calculus system ("0", "1" and "2"), but the binary still won.

Perhaps the victory went to her, because the USSR fell apart, and maybe because "0" and "1" is easier to present in the form of electrical signals. So, digital devices based on a binary calculus system are easier and cheaper produced. Read more about binary numbers later.

Digital structure structure

Almost in each digital device there are typical elements, from the combination of which it consists. Some elements are completely simple, some more complex, and some very complex. In amateur practice, most often found: triggers, timers, counters, registers, microcontrollers, comparators, etc.

Let's choose something from this list and see how it is arranged. Let it be a microcontroller (MK)! Okay, I confess. Microcontroller I chose no accident. The fact is that it is the appearance of microprocessors that produced a real revolution in electronics and put forward its development to a new level.

MK is the most numerous and popular view of microprocessors in the world. Its special makes that the microcontroller is a micro-PC - a whole computer in one chip. Imagine a computer size, for example, with a penny. This is the MK.

Microcontrollers are used everywhere: in modern TVs, refrigerators, tablets, security systems. Wherever you manage to manage something, the microcontroller can find its place. And all due to the fact that, like any microprocessor, MK can be programmed. As a result, the same type of chip can be used in hundreds of different devices.

Nowadays, for example, AVR, PIC, ARM microcontrollers are most popular. Each of the companies, which produces the listed types of MK, produces dozens, if not hundreds, varieties of microcontrollers intended for all conceivable and inconceivable tasks.

How the microcontroller works

Despite the complexity of the design of the real microcontroller, to tell how it functions can be only one sentence: "The text of the program is recorded in the microcontroller's memory, the MK reads the commands from this program and performs them," that's all.

Of course, MK cannot perform any teams. He has a basic set of teams that he understands and knows how to perform. Combining these commands, you can get almost any program with which the device will do exactly what they want from it.

In the modern world, the microprocessor (MK is also a microprocessor, but specialized) can have either a lot of basic teams or very little. This is such a conditional separation for which two terms have even come up with: CISC and RISC. CISC is a lot of different types of teams for all occasions, RISC is only the most necessary and frequently used commands, i.e. Reduced set of commands.

Most microcontrollers are confirmed by RISC. It is explained by the fact that when using a reduced set of microcontrollers, the microcontrollers are easier and cheaper for production, they are easier and quickly mastered the developers of instruments. There is a lot of differences between CISC and RISC, but now it is fundamentally important to remember only that CISC is a lot of teams, RISC is few teams. Deeper with these two ideas will get acquainted some other time.

What happens when the microcontroller turns on?

So, let's imagine the perfect world in which you have MK and the program has already been recorded in his memory. Or, as they usually say, MK "stitched" (in this case, the program is called "firmware") and ready for battle.

What happens when you serve meals to your scheme with MK? It turns out nothing special. There is no magic at all. There will be the following:

After powering, the microcontroller will go to watch what is in memory. At the same time, he "knows" where to watch to find the first team of his program.

The location of the start of the program is established in the production of MK and is never changed. MK considers the first command, will execute it, then he considers the second team, will execute it, then the third and so to the last. When he considers the last team, then everything will begin first, since the MK performs the program in a circle, if he did not say. So it works.

But it does not interfere with writing complex programs that help control refrigerators, vacuum cleaners, industrial machines, audio players and thousands of other devices. You can also learn how to create devices with MK. It will take time, desire and a little money. But these are such little things, right?

How is a typical MK

Any microprocessor system stands on three whales:

1. CPU (Alu + control device),
2. Memory (ROM, RAM, Flash),
3. I / O ports .

The processor using I / O ports receives / sends data in the form of numbers, produces various arithmetic operations over them and maintains them into memory. Communication between the processor, ports and memory performs on wires called tire (Tires are divided into several types of destination) . This is the overall idea of \u200b\u200bthe work of the MP system. That's how in the picture below.

MK, as I already wrote, also a microprocessor. Just specialized. The physical structure of the MK microcircuits of different series can differ significantly, but ideologically, they will also be similar and will have such, for example, blocks like: ROM, RAM, Alu, I / O ports, timers, counters, registers.

The modern scale of the development of digital electronics is so huge that even for each item from this table, you can write a whole book, or even one. I will describe the basic ideas that will help you easily understand in more detail in each of the devices.

Brain microcontroller

The microprocessor / microcontroller always works on the program embedded in it. The program consists of a sequence of operations that MK can perform. Operations are performed in the CPU - this is a microcontroller brain. It is this body that can produce arithmetic and logical operations with numbers. But there are four more important operations that he knows how to do:

• reading from the memory cell
• recording in the memory cell
• reading from the port in / in
• record to port in / in

These operations are responsible for reading / writing information into memory and into external devices via I / O ports. And without them, any processor is tested in useless trash.

Technically, the processor consists of Allu (Calculator of the processor) and a control device that religates the interaction between the I / O ports, memory and arithmetic and logic device (ALU).

Memory microcontroller

Earlier in the table with typical devices included in the MK, I indicated two types of memory: ROM and RAM. The difference between them is that the data is saved between the inclusions of the device. But at the same time ROM (ROM) is quite slow memory. Therefore, there is RAM (RAM), which is rather fast, but can storing data only when power is applied to the device. It is necessary to turn off the device and all data from there ... PSHICK and NO.

If you have a laptop or a personal computer, then you know such a situation: wrote the mountain of the text, I forgot to keep it on a hard disk, the electricity suddenly disappeared. Turn on the computer, but there are no text. That's right. While you wrote him, he was kept in RAM. Therefore, text and disappeared with a computer shutdown.

In the foreign world of RAM and ROM call RAM and ROM:

1. RAM (Random Access Memory) - memory with random access
2. ROM (read only Memory) - read only memory

We are also called energy-dependent and non-volatile memory. What in my opinion more accurately reflects the nature of each type of memory.

ROM.

Now more and more got the distribution of the ROM to the memory of type Flash (or, in our opinion, ESPMU). It allows you to save data even when the device is turned off. Therefore, in modern MK, for example, Flash-memory is used as a ROM to the AVR MC.

Previously, the ROM memory chips were one-time programmable. Therefore, if a program or data with errors were recorded, then such chips simply missed. A little later came the ROM that could be overwritten repeatedly. These were chips with ultraviolet erasing. They lived quite a long time and are even now found in some devices from the 1990s ... 2000s. For example, this is the ROM of the USSR.

They had one substantial minus - with randomly illumination of the crystal (the one that is visible in the window) could be damaged. And the ROM still works slower than RAM.

Oz

RAM unlike ROM, PPZ and ESPMU is energo-dependentand when the power is turned off the device, all data in RAM disappear. But no microprocessor device does not do without it. Since during the work required somewhere to store the results of the calculations and the data that the processor works with. ROM for these purposes is not suitable because of its slowness.

Memory of programs and data memory

In addition to separation on energy-dependent (RAM) and non-volatile memory in microcontrollers, there is a division into data memory and memory of programs. This means that the MK has a special memory, which is intended only for storing the MK program. In today's times, this is usually Flash ROM. It is from this memory that the microcontroller reads the commands that perform.

Separately from the memory of the programs there is a data memory in which the intermediate results of the work and any other data required by the program are placed. Memory of programs is the usual RAM.

Such a separation is good because no error in the program can damage the program itself. For example, when, by mistake, MK will try to record a random number in the program in the program. It turns out that the program is reliably protected from damage. By the way, this separation has its own very name - "Harvard Architecture".

In the 1930s, the US government commissioned Harvard and Prince Universities to develop architecture EUM for naval artillery. In the late 1930s, at Harvard University, Howard Eiken was developed architecture Computer Mark I, hereinafter referred to as this university.

Below I sketchily depicted Harvard architecture:

Thus, the program and data with which it works is physically stored in different places. As for large processor systems such as a personal computer, then in them the data and the program during the operation of the program are stored in the same place.

Memory hierarchy

How the microcontroller brain is arranged

You already mean that the MK brain is the CPU - a central processor, which consists of Alu (arithmetic-logical device) and control devices (UU). Uu religates all orchestra from memory, external devices and alu. Thanks to him, MK can execute teams in the order in which we want it.

Alu is a calculator, and Hu tells Alu what, with what, when and in which sequence is calculated or compared. Alu knows how to add, deduct, sometimes share and multiply, to flip logical operations: and, or, not (they will be a little later)

Any computer, MK, including, can work today only with binary numbers composed of "0" and "1". It is this simple idea that led to a revolution in the field of electronics and explosive development of digital technology.

Suppose that Allu must be folded two numbers: 2 and 5. In simplified form it will look like this:

At the same time, the UU knows in which memory place to take the number "2", in which number "5" and in which place of the memory place the result. Uu knows about everything because it read about it in a team from the program that was currently read in the program. In more detail about the ranges of binary numbers and how the adder Alu from the inside is arranged, I will tell a little later.

Well, you will tell you, what if you need to get these numbers not from the program, but from outside, for example, from the sensor? How to be? Here in the game and enter the I / O ports, with which MK can receive and transmit data to external devices: displays, sensors, motors, valves, printers, etc.

Logical operations

Do you probably know the comic statement about "female logic"? But it will not be about her, but logic in principle. The logic operates with causal relationships: if the sun rose, it became light. The reason the "sun rose" caused the result "was light". At the same time, we can say about every statement "Truth" or "Lie".

For example:

• "Birds float under water" - this is a lie
• "Water wet" - at room temperature this statement is true

As you noticed, the second statement under certain conditions can be both true and false. In our computer there are only numbers and engineers with mathematic collections invented signify the truth "1", and the lies "0". This made it possible to record the truth of approval in the form of binary numbers:

• "Birds float under water" \u003d 0
• "Wet wet" \u003d 1

And such a record allowed mathematicians to carry out entire operations with these statements - logical operations. The first to do it was thought of George Boule. By whose name and named such an algebra: "Bulev Algebra", which turned out to be very convenient for digital machines.

The second half alu is logical operations. They allow you to "compare" allegations. Basic logical operations are only a few pieces: and, or, not, but this is enough, since more complex can be combined from these three.

Logical operation AND indicates simultaneity of statements, i.e. That both statements are true at the same time. For example, the statement it will be truly only when both simpler statements are true. In all other cases, the result of the logical operation and will be false

Logical operation OR It will be true if at least one of the statements participating in the operation will be truly. "Birds float under water" and "Wet Wet"true, since true statement "Wet Wet"

Logical operation NOT Changes the truth of approval to the opposite value. This is a logical denial. For example:

The sun comes off every day \u003d truth

No (the sun comes off every day) \u003d not truth \u003d lies

Thanks to the logical operation, we can compare binary numbers, and since our binary numbers always indicate something, for example, some signal. It turns out that thanks to milking algebra, we can compare real signals. This is the logical part of Allu and is engaged.

I / O device

Our MK must communicate with the outside world. Only then will it be a useful device. To do this, MK has special devices that are called I / O devices.
Thanks to these devices, we can send signals from sensors, keyboards and other external devices to a microcontroller. A MK after processing such signals will send through the output devices, with which you can adjust the engine speed or the brightness of the lamp luminescence.

Let's summarize:

1. Digital Electronics - Alevision Auxberg Electronics
2. Digital device knows and understands only numbers
3. Any information: message, text, video, sound, - can be encoded with binary numbers
4. The microcontroller is a microcomputer on the same chip
5. Any microprocessor system consists of three parts: processor, memory, I / O devices
6. The processors consists of alu and control device
7. Alu knows how to perform arithmetic and logical operations with binary numbers

Stay with us. In the following articles, I will tell in more detail how the memory of the MK, I / O ports and Allu are arranged. And after that, we will go even further and in the end it comes to the analog electronics.

p.S.
Find a mistake? Tell me!

Big Radio and Program Designer

Studying the basic elements of digital electronics We will start with the most simple, and then we will consider increasingly complex. Examples of the use of each next item will be based on all the elements previously discussed. Thus, the main principles of building enough complex digital devices will be gradually given.

Logic elements (or, as they are also called, valves, "Gates") are the most simple digital chips. It is in this simplicity that consists of their difference from other microcircuits. As a rule, in one case, the chip can be located from one to six of the same logical elements. Sometimes different logical elements can be located in one case.

Usually, each logical element has several inputs (from one to twelve) and one output. In this connection between the output signal and input signals (truth table) is extremely simple. Each combination of the input signals of the element corresponds to the level of zero or units at its output. There are no internal memory in the logical elements, so they relate to the group of so-called combinational chips. But, unlike more complex combination chips, considered in the following lecture, logical elements have inputs that cannot be divided into groups that differ in the functions performed by them.

The main advantages of logical elements, compared to other digital chips, are their high speed (small delays), as well as low power consumption (small consumption current). Therefore, in cases where the required function can be implemented solely on logical elements, it always makes sense to analyze this option. The lack of them is that based on them is quite difficult to realize any complex functions. Therefore, most often logical elements are used only as a supplement to more complex, to more "smart" microcircuits. And any developer usually seeks to use them as little as possible and as much as possible. There is even the opinion that the skill of the developer is inversely proportional to the number of logical elements used by it. However, this is right not always.

Inverters

The easiest logical element is an inverter (the logical element is not, "Inverter"), already mentioned in first lecture. The inverter performs the simplest logical function - inverting, i.e., change the input level to the opposite. It has only one input and one way out. The output of the inverter may be type 2c or OK type. On the fig. 3.1. The conventions of the inverter adopted with us and abroad are shown, and in table. 3.1. The truth table of the inverter is presented.

Fig. 3.1. Legend inverters: foreign (left) and domestic (right)

In one case, the microcircuit usually there are six inverters. Domestic designation inverters chip - "LN". Examples: KR1533LN1 (SN74ALS04) - Six inverters with 2C, CR1533LN2 (SN74ALS05) - six inverters with OK output. There are also inverters with an output OK and with an increased output current (LN4), as well as with an elevated output voltage (LN3, LN5). For inverters with an output OK, it is necessary to turn on the output load resistor Pull-Up. Its minimum value can be calculated very simple: R< U/I OL , где U - напряжение питания, к которому подключается резистор. Обычно величина резистора выбирается порядка сотен Ом - единиц кОм.

Two main areas of use of inverters are a change in signal polarity and a change in the polarity of the signal front (Fig. 3.2). That is, from a positive input signal, the inverter makes a negative output signal and vice versa, and from the positive front of the input signal - the negative front of the output signal and vice versa. Another important use of the inverter is a signal buffering (with inversion), that is, an increase in the load capacity of the signal. This happens when some signal must be submitted on a lot of inputs, and the output current of the signal source is insufficient.

Fig. 3.2. Inversion of the polarity of the signal and the inversion of the polarity of the signal front

It is the inverter as the simplest element, more often than other elements is used in non-standard inclusions. For example, inverters usually apply in rectangular pulse generator schemes (Fig. 3.3), the output of which is periodically changing from the zero level per unit and back. All the diagrams, except for the circuit D, are made on the elements of K155LN1, but can also be implemented on inverters of other series with the corresponding change in resistor ratings. For example, for the K555 series, the ratings of the resistors increase approximately three times. Scheme D is made on the elements of the KR531LN1, as it requires high speed of inverters.

Fig. 3.3. Pulse generator schemes on inverters

Schemes A, B and B are conventional RC generators whose characteristics (output frequency, pulse duration) can only be calculated approximately. For scheme A and B under the indicated size of the resistor and the condenser, the generation frequency will be about 100 kHz, for a circuit B - about 1 MHz. These schemes are recommended to use only in cases where the frequency is not too important, and the very fact of generation is important. If the exact frequency value is fundamentally, it is recommended to use schemes G and D, in which the frequency of the output signal is determined only by the characteristics of the quartz resonator. The scheme g is used for a quartz resonator operating on the first (main) harmonic. The amount of capacity can be estimated by the formula:

where F is the generation frequency. Diagram D is used for harmonic quartz resonators, which operate at frequency, greater main 3, 5, 7 times (this is necessary for generation frequencies above 20 MHz).

Fig. 3.4. Using inverters for signal delay

Inverters also apply in cases where it is necessary to obtain a signal delay, the truth is minor (from 5 to 100 ns). To obtain such a delay, the desired number of inverters ( fig. 3.4., top). Total delay time, for example, for four inverters, can be estimated by the formula

tZ \u003d 2T PHL + 2T PLH

True, it must be borne in mind that usually real delays of elements are significantly lower (sometimes even twice) than table parameters T PHL and T PLH. That is, it is not necessary to talk about the exact value of the resulting delay, it can only be estimated approximately.

Condensers are also used to delay the signal (Fig. 3.4, bottom). At the same time, the delay occurs due to the slow charge and discharge of the capacitor (voltage on the condenser - UC). The scheme without a resistor (left in the figure) gives a delay of about 100 ns. In the diagram with the resistor (right in the figure), the rating of the resistor should be the order of hundreds. But when choosing such schemes with condensers, it is necessary to take into account that some series of chip (for example, kr1533) do not work well with the protracted fronts of the input signals. In addition, it should be borne in mind that the number of current capacitors in the scheme is inversely proportional to the level of scheme developer skill.

Finally, another use of inverters, but only with the OK output, is to build on their basis the so-called "wired or" elements. To do this, the outputs of several inverters with OK outputs are combined, and through the resistor are attached to the power source. (Fig. 3.5). The output of the circuit is the combined output of all elements. This design performs a logical function or is not, that is, the output will be a logical unit signal only at zeros at all inputs. But the logical functions will be described in more detail below.

Fig. 3.5. Combining inverter outputs with OK for function or non

In conclusion, it should be noted that the signal inversion is used in more complex logical elements, as well as inside digital chips performing complex functions.

Repeators and buffers

Repeators and buffers differ from the inverters primarily by the fact that they do not invert the signal (though there are inverting buffers). Why then do they need? First, they perform the function of increasing the load capacity of the signal, that is, they allow you to submit one signal on a lot of inputs. For this, there are buffers with elevated output and 2c output, for example, LP16 (six buffer repeatters). Secondly, most buffers have an output OK or 3C, which allows them to be used to obtain bidirectional lines or for multiplexing signals. Let us explain in more detail these terms.

Fig. 3.6. Bidirectional line

Under bidirectional lines are subject to such lines (wires), signals for which can be distributed in two opposite directions. Unlike unidirectional lines that go from one output to one or several inputs, several outputs can be connected to a bidirectional line and several inputs. (Fig. 3.6). It is clear that bidirectional lines can only be organized based on OB or 3C outputs. Therefore, almost all buffers have exactly such outlets.

Fig. 3.7. Unidirectional multiplexed buffer-based line

Multiplexing is called the transfer of different signals over the same lines at different times. The main goal of multiplexing is to reduce the total number of connecting lines. The bidirectional line is necessarily a multiplexed, and the multiplexed line can be both unidirectional and bidirectional. But in any case, several outlets joins it, only one of which is in an active condition at each moment. The remaining outputs are disconnected at this time (translated into a passive state). In contrast to the bidirectional line, only one input can be connected to a multiplexed line, but be sure to several outputs with OK or 3C. (Fig. 3.7). Multiplexed lines can be built not only on buffers, but also on multiplexers chips, which will be considered in lectures 5, 6.

Fig. 3.8. Combining buffer outputs with ok

An example of buffers with an output OK is a LP17 chip (six buffers about OK). Just as inventors with OK (See Fig. 3.5)The outputs of multiple buffers with OK can be combined to obtain the "mounting and" function, that is, the output will signal a logical unit only when units at all inputs (Fig. 3.8). That is, the current element I. is being implemented

Buffers with yield 3c are represented by much more chip, for example, LP8, LP11, AP5, AP6, AP14. These buffers necessarily have the EZ (or OE) control input, which translates the outputs in the third, passive state. As a rule, the third state corresponds to the unit at this input, and the active state of the outputs is zero, that is, the EZ signal has a negative polarity.

Buffers are unidirectional or bidirectional, with inverses or without signal inversion, with control of all outputs simultaneously or with control of output groups. All this is determined by a wide variety of buffer microcircuits.

The simplest unidirectional buffer without inversion is the LP8 microcircuit (four buffers with type 3 Outputs and separate control). Each of the four buffers has its own EZ permission. The truth table is very simple (Table 3.2): At a zero signal at the control input, the output repeats the input, and when the output is disabled. This chip is conveniently used to process single signals, that is, to repeat the input signal with the ability to turn off the output.

Fig. 3.9. Application buffer with 3c as buffer with ok

These same buffers are sometimes convenient to use to replace buffers with the output OK (Fig. 3.9). In this case, the control input serves as an informational entrance. At zero at the inlet, we get zero at the output, and with a unit at the input - the third state at the output.

Fig. 3.10. Multiplexing two input codes using buffers with 3c

It is very often necessary to process non-single signals, but a group of signals, for example, signals transmitting multi-digit codes. In this case, it is convenient to use group control buffers, that is, having one EZ permission input for multiple outputs. Examples can serve as chips LP11 (six buffers divided into two groups: four and two buffers, for each of which there is a control input) and Ap5 (eight buffers, divided into two groups of four buffer, each of which has its own control) .

On the fig. 3.10 An example of multiplexing of two eight-bit codes is shown using two AP5 microcircuits. The outputs of both microcircuits are combined with each other. The transmitting to the output of each of the two input codes is allowed by its control signal (Ex. 1 and Ex. 2), and the simultaneous arrival of these two signals must be excluded so that there are no conflicts on the outputs.

Fig. 3.11. Enable bidirectional buffer

Bidirectional buffers, unlike unidirectional, allow you to transmit signals in both directions. Depending on the special control signal T (Other designation - BD), the inputs may become outputs and vice versa: outputs - inputs. It is necessarily available to the input of the third state of EZ, which can turn off both the inputs and outputs.

On the fig. 3.11 An example is shown bidirectional buffer an AP6, which can transmit data between two bidirectional tires A and B in both directions. With a single level on the control input T (out.) The data is transmitted from the bus A to the bus B, and at a zero level - from the tire b to the tire A (Table 3.3). Single level on the EZ control input (signal off) disables the chip from both tires.

Bidirectional transmission can be organized on the basis of unidirectional buffers. On the fig. 3.12. It is shown how this can be done on two microcircuits AP5. Here at the zero signal of the UPR. 1 The information will be transmitted from the bus A to the B tire, and at a zero signal at the input UPR. 2 - from the tire to the Tire A. If both entrances are UPR. 1 and UPR. 2 are in a single state, then the tires A and are disabled from each other, and the feed of zeros on both inputs of the UPR. 1 and UPR. 2 must be excluded, otherwise the state of both tires A and B will not be determined.

Fig. 3.12. Organization of bidirectional transmission using unidirectional buffers

Buffer chips in domestic series have a variety of designations: LN, LP, AP, IP, which sometimes makes it difficult to choose from. For example, LN6, LP8, LP11, AP5, AP6, IP5, IP6. Buffers with LN letters have inversion, UP buffers and IP can be inversion and without inversion. All parameters at buffers are pretty close, the difference is in inversion, in the number of discharges and in the control signals.

The temporal parameters of the buffers include in addition to the signal delay from the information input to the information output, also delayed the exit transition to the third state and from the third state to the active state (T PHZ, T PLZ and T PZH, T PZL). The values \u200b\u200bof these delays are usually about twice as much as the values \u200b\u200bof delays between the information entrance and the output.

The disconnected output of buffers (both OK and 3C) requires the use of load resistors. Otherwise, the input connected to the disconnected output turns out to be suspended, as a result of which the scheme may not work unstable, to malfunctions. Connecting a resistor in the case of OK (Pull-Up) is performed by the standard method. (See Fig. 3.8). Similarly, a resistor between 3C and supply voltage can be included. (Fig. 3.13)Then, when the output is disabled, the logical unit will arrive. However, it is possible to include a resistor between the output and the earth, then the logical zero signal will arrive when the output is turned off. The inclusion of two resistors (resistive divisor) is also applied, while the value of the upper resistor (connected to the power supply) is usually selected 2-3 times less than the lower resistor (attached to the "land"), and the value of the parallel interconnected two resistors is chosen equal to Approximately 100 ohms. For example, resistors may have 240 Ohm and 120 Ohm ratings, 360 ohms and 130 ohms. A disconnected output is perceived in this case attached to it as a unit.

Fig. 3.13. The inclusion of resistors at the outlet of the buffers 3c

Sometimes 3C resistors are connected to the outputs at all, but in this case it is necessary to ensure that the subsequent input perceives the signal from exit 3C (that is, reacts to it) only when the output is in an active condition. Otherwise, malfunctions and failures in the device are possible.

Fig. 3.14. Application buffers for indication

Another typical use of buffers associated with their large output currents is the LED display. LEDs can be connected to the buffer output by two main ways. (Fig. 3.14). With the first of them (on the left in the figure), the LED is on, when the output 3c or 2c-signal is a logical unit, and at the second (right in the figure) - when the logical zero signal is OK. The size of the resistor is selected based on the characteristics of the LED, but is usually about 1 com.

Elements and, and no, or, or not

The next step towards the complication of digital electronics components is the elements that perform the simplest logical functions. Combines all these elements that they have several equal Inputs (from 2 to 12) and one output, the signal on which is determined by the combination of input signals.

The most common logical functions are (in the domestic system of symbols - whether), and not (denoted by LA), or (denotes ЛЛ) and or-no (denoted by LL). The presence of a word is not in the name of the element indicates only one - the built-in signal inversion. The international designation system uses the following abbreviations: and - function and, nand - function and non, or - function or, Nor - function or non.

The name of the functions themselves and or or indicates whether the output signal appears at the inputs. It is important to remember that in this case it is about positive logic, about positive, single signals at the inputs and at the output.

The element and generates a unit at the output if and only if at all its inputs (and on the first, and on the second, and on the third, etc.) there are units. If we are talking about the element and not, zero is formed at the output when at all inputs - units (Table 3.4). The digit before the name of the function indicates the number of element inputs. For example, 8i is not an eight-time element and with an output inversion.

An element or generates zero at the outlet then and only if at all inputs zero. The element or-does not give the output zero if you have at least one of the inputs of the unit ( table. 3.4.). An example of the designation: 4Ili-not - four-hundred-to-line element or with an output inversion.

Fig. 3.15. Designations of elements and, and non, or, or nonsense: foreign (left) and domestic (right)

Domestic and foreign designations in the diagrams of two-line elements and, and no, or, or not shown on fig. 3.15. All these elements are with the outputs of type 2c, OK and 3C. In the latter case, there is a permissions input.

It is not difficult to notice (See Table 3.4)that in the case of negative logic, at zero input and output signals, the element and performs the function or, that is, there will be zero at the output in the case when at least one of the inputs zero. And the element or under negative logic performs the function and, that is, the output will be zero only when zeros are present at all inputs. And since in real electronic devices, signals can be any polarity (both positive and negative), then it is always very good to choose the element required in each case. Especially it is important to remember when several multi-dimensional logical elements with inversion and without a complex function are consistently connected.

Therefore, elements and, and not, or, or non-developer, it is far from always convenient to apply exactly how logical functions specified in their name. Sometimes it is more convenient to use them as permissions / prohibition or mixing / coincidence. But first we will consider cases of implementing the logical functions on these elements.

On the fig. 3.16 Examples of the formation of output signals on the basis of the required time diagrams of the input and output signals are given. In the case, the output signal should be equal to one at two single input signals, therefore, it is enough to be element 2. In the case of B, the output signal must be zero, when at least one of the input signals is equal to one, therefore, it is required to be element 2 or not. Finally, in the case of the output signal, it must be zero with the simultaneous arrival of the unit signal of the BX. 1, zero signal of the WX. 2 and a single signal of the WX. 3. Consequently, it is required element 3 and non, and the signal of the WX. 2 You must first sign.

Fig. 3.16. Examples of the use of elements and or or

Any of the logical elements of the group under consideration can be considered as a controlled input signal flow (with or without inversion).

For example, in the case of an element 2, not one of the inputs can be considered information, and the other is the managers. In this case, with a unit on the control input, the output signal will be equal to the input signal to the input signal, and at zero on the control input, the output will be constantly equal to one, that is, the passage of the input signal will be prohibited. Elements 2I - not with OK output often use precisely as managed buffers to work on a multiplexed or bidirectional line.

In the same way as elements and, or, or not (Fig. 3.17). The difference between the elements consists only in the polarity of the control signal, in the inversion (or its absence) of the input signal, as well as in the level of the output signal (zero or unit) while prohibiting the passage of the input signal.

Fig. 3.17. Permission / prohibition of signals passing on elements and, and no, or, or not

Fig. 3.18. Appearance of an excess front when the input signal is prohibited

When using permissions / prohibition elements, additional problems may occur in the case when the signal from the output of the element goes to the input reacting to the front of the signal. At the time of transition from the resolution status to the prohibition state and from the prohibition state, an additional front may appear in the output signal state, an additional front may appear, in no way associated with the input signal (Fig. 3.18). To this not happen, you need to follow the next simple rule: if the input responds to a positive front, then in the output state of the element, there should be zero, and vice versa.

Sometimes it is necessary to implement the mixing function of two signals for one or another polarity. That is, the output signal is to be produced both in the arrival of one input signal and when the arrival of another input signal. If both input signals are positive and positive output, then we have a clean function or, and the element 2. However, with negative input signals and a negative output signal, the element 2 is needed for the same mixing. And if the polarity of the input signals does not coincide with the desired polarity of the output signal, then the elements are needed with inversion (and not at positive output signals and or not at negative output signals). On the fig. 3.19 The mixing options are shown on different elements.

Fig. 3.19. Implementation of mixing two signals

Finally, the elements under consideration and, and no, or, or, not sometimes it can be conveniently used as the coincidence schemes of various signals. That is, the output signal should be generated when the signals on the inputs coincide (come simultaneously). If there is no coincidence, then the output signal must be missing. On the fig. 3.20the variants of such coincidence schemes on four different elements are shown. They differ in the polarities of the input signals, as well as the presence or absence of an output signal inversion.

Fig. 3.20. Coincidence schemes of two signals

Consider two examples of the sharing of elements and, and no, or, or no. fig. 3.21).

Fig. 3.21. Examples of sharing elements

Let it be necessary to mix two signals, each of which can be allowed or prohibited. Let the polarity of the input signals and the resolution signals are positive, and the output signal must be negative. In this case, you need to take two two-axis elements and mix their output signals using a two-input element or non (A).

Let it be necessary to mix two negative signals and one positive signal, and the resulting signal can be allowed or denied. The polarity of the resolution signal is negative, the polarity of the output signal is negative. To do this, take a three-hundredth element and, inverter for a negative input signal and two-way element or (b).

Elements and, and no, or, or no, can also be used as inverters or repeaters (Fig. 3.22)For which it is necessary to combine the inputs or to the unused inputs to submit the desired level signal. The second is preferable, since the input combining not only increases the input current, but also slightly reduces the speed of the elements.

Fig. 3.22. Inverters and repeaters

Fig. 3.23. Microcircuit on and inputs

For functions and often combine the inputs of more complex chips. In other words, some function is performed only when there are signals of the necessary polarity on all combined software and inputs. Most often, the CS chip selection and inputs of the third state of the EZ chip output inputs are also combined. On the fig. 3.23 The three examples of such an association were shown by I. In this case, it is necessary to take into account that zero signals should be received on the inverse inputs to perform the function, and single signals should be included. Examples can serve as chips KR556T44, KR556T5, KR1533Ap14, kr1533Ap15.

Until now, considering elements and, and no, or, or no, we did not go beyond the first level of presentation (logical model). This is quite acceptable in the case when the input signals of the elements do not change simultaneously or almost simultaneously when their fronts are spaced out of time (more than at the time of the delay of the element). With the simultaneous change in the input signals, everything will be much more complicated. It is necessary to attract the second and sometimes the third level of the presentation. At the time of changing the input signals, the output signal becomes uncertain, unstable, unpredictable. As a result, with incorrect design, all complex scheme may not work, an entire device or even a large system.

For example, take the logical element 2I - not. Suppose that there are signals that change simultaneously at the inputs, and in antiphase, that is, one switches from zero per unit, and the other is from the unit to zero. Let for one reason or another (due to the transfer by wires, due to different delays in the elements, etc.) one of the signals slightly moved over time relative to the other (Fig. 3.24). At the same time, two single signals will be present on two inputs during the short-term period. As a result, the output will start switching from a unit to zero. He may have time to switch, and then a short impulse is formed. He may not have time to switch, and then the impulse will not. It can sometimes have time to switch, and sometimes you do not have time, and then the output pulse will appear, it will not be. It all depends on the speed of the element and the delay value. The latter situation is most unpleasant, as it can cause an unstable malfunction, to identify which is extremely difficult.

Fig. 3.24. Short pulse at the output of the element 2I - not

As an example, take one of the most common applications of the elements in question and, and non, or, or non-selection of codes. The essence of selection is reduced to the following. Let there be some tire by which codes are transmitted. It is necessary to identify any specific code on this bus, that is, to form an output signal corresponding to the desired input code.

Fig. 3.25. Selection of gating codes

The scheme performing such a function is quite simple (Fig. 3.25). It is based on inspection elements and not. At the same time, the signals corresponding to the category discharges on which the units must be applied directly to the inputs of elements and non. And the signals corresponding to the discharges of the code on which must be zeros are fed to the inputs of elements and not through the inverters. The output signals of the elements and are not combined with the element or non. As a result, the output of the element or is not formed a signal. 1 At that time, when the desired code is present at the input.

More information on synchronization will be told in the following lectures.

However, there are cases where the specified feature of the elements and, and not, or, or not to form short pulses when the input signals change its very useful. For example, we need to form a short impulse on a positive or negative front of the existing signal. Then this signal is inverted, specifically delayed using the chain of elements or containers and feed the source and the delayed signal to the inputs of the element (Fig. 3.26).

Fig. 3.26. Short pulse formers on the front of the input signal

The pulse on the positive front of the input signal is formed on the element 2 and 2 or (A), and the pulse on the negative front of the input signal is on the 2 liter element or 2 or no (b). If an element with inversion, then the output pulse will be negative, if without inversion, then positive. With the capacity indicated in the diagrams, the pulse duration is about 50 ns. To increase the pulse duration, it is necessary to increase the size of the tank or the number of inverters in the delay circuit (the number of inverters must be odd).

Ministry of Russian Federation

Tomsk Polytechnic University

__________________________________________________________________

E.L. Dog

Digital circuit engineering

Tutorial

UDC 681.325.6

Dog E.L. Digital circuit engineering. Studies. benefit. Ch.I. Tomsk: ed. TPU, 2002. - 160c.

The manual contains the main questions of the course of lectures for students of the specialty 210100 management and computer science in technical systems. The manual was prepared at the Department of Automatics and Computer Systems TPU, corresponds to the discipline curriculum and intended for students of the Institute of Remote Education.

Printed by the Decree of the Editorial Publishing Council of the Tomsk Polytechnic University

Reviewers:

V.M. Dmitriev Professor, Doctor of Technical Sciences, Head of the Department of Theoretical Fundamentals Electrical Engineering Tomsk University of Management and Radio Electronics Systems;

S.I. Korolev director of NPO NPO "Spetstehauditservis",

candidate of Technical Sciences, Senior Researcher.

Templan 2002.

Tomsk Polytechnic University, 2002

Introduction

This tutorial is intended for students of higher educational institutions, studying in the specialty 210100 "Informatics and Management in Technical Systems". It is drawn up on the basis of the course of lectures read by the author at Tomsk Polytechnic University for a number of years, and is devoted to a systematic presentation of methods for formalized construction of digital equipment on widescaming chips.

The discipline "Digital circuitry" should be considered as a continuation of the "Electronics" course, which students must learn before, as the knowledge of the element base of the analog electronic devices is required.

Most of the modern automation systems, computing systems, transmission and processing systems are performed on digital equipment devices or completely or partially. Therefore, the knowledge of the principles of applying digital devices and the construction on the basis of these systems of various purposes is relevant and greater practical value in both engineering activities and in a methodological studies.

The material of the benefit can be divided into three parts: 1) the bases of microelectronics; 2) combinational devices of digital technology; 3) Digital technology sequence logic devices.

Starting to master the course, the material should be studied in the order of transfer of these parts, since the subsequent material is based on the knowledge of the previous one, and the change in the sequence can lead to difficulties in his assimilation. It is further aggravated by the fact that various terms and concepts are used in other teaching aids and special technical literature to explain the same phenomena, processes performed by transformations, etc. The difference in the concepts used or their incorrect leads to a lack of understanding of the essence of the outlined material and, as a result, the emergence of difficulties in his assimilation.

The first two of these sections entered the first part of the present benefit (F). A separate manual is devoted to the third section.

IN 1. Application of digital devices

Currently, in connection with the creation and widespread implementation of microprocessor devices and systems into the engineering practice, it is not weakened and an interest in digital methods of processing and transmitting information is stimulated. These methods, in turn, give systems a number of positive properties and qualities. The loyalty of the transmitted information increases, the high speed and performance of information processing systems is achieved, the cost is ensured, high reliability, low energy consumption, etc.

The tasks solved by these systems are very diverse and predetermine the functions of devices that form a specific system. Therefore, devices and their functions are advisable to be considered in the light of the tasks that are solved by systems and, in particular, those subtasks that are performed by individual devices or blocks.

Basic typical tasksarising from automatic or automated management and control by industrial or other processes are:

collectioninformation (its receipt);

conversion information (scaling, normalization, filtering, coding, etc.);

transmission-reception information;

processing and use information;

storageinformation.

Depending on the target and the main functions distinguish:

Automatic (or automated) control and control systems.

Information transmission systems.

Information processing systems (computing systems).

To understand the relationship of the specified tasks, the location and role of electronic digital devices used in these systems, consider the generalized structural schemes of these systems and the functional purpose of their components.

B1.1. Automatic control systems

To govern means to know the status (position) of the managed object and in accordance with the specified algorithm ( control algorithm) Influence the object, seeking to eliminate the deviations.

Therefore, management is generally due to the following actions:

obtaining information about the state of the object;

comparing the received information with the specified information about the state of the object;

formation of control signals (impacts);

impact on the object in order to bring it to the desired condition.

In accordance with the listed actions into the automatic control system (SAU), in the general case, an information and measurement device, a control device and an actuator (Fig. B1) should be included.

Information and measuring device (IIU) receives information about the control object (OU) and pre-it processes it. Obtaining information is to form primary signals, the values \u200b\u200bof which are proportional to the values \u200b\u200bof the parameters characterizing the state of the OU. Under the property can be understood as a separate production plant and the production process as a whole. And under the "output coordinates" of the object. This can be, for example, the values \u200b\u200bof temperature, pressure, consumption of materials or energy, and the like. Since most of these coordinate parameters are represented in analog form and are characterized by an infinite set of values, the signals must be normalized by their parameters, scaled and have a unified form.

Therefore, the primary measuring transducers and sensors, analog-to-digital converters and other functional nodes, with which the following transformations are performed are in the IIU.

values \u200b\u200bof physical quantities into unified analog signals of direct or alternating current;

scaling or rationing signals in terms of level and form;

converting analog signals to discrete (digital) signals;

signal coding and some other conversion.

The signals about the current values \u200b\u200bof the coordinates come to control device (UU). The function of this device includes a comparison of current values \u200b\u200bwith specified coordinate values \u200b\u200band the formation of the comparison of the control signals (control signals). The specified values \u200b\u200bcan be entered by a human operator or automatically programmatically. In the first case, an automatic regulator or several automatic regulators can be used as a UU, which determines and asks a person. In the second case, the UU is a microevm software automatic machine and the role of the operator's person comes down to entering the program and the initial start-up of the system.

To perform the specified functions from the WU, it is required to perform arithmetic and logical operations to calculate the values \u200b\u200band comparing signals, short-term and long-term memorization (storage) of signals and the formation of control unified signals. The latter contain information on the basis of which the impact on the control object (control exposure) are formed, leading it to the desired state.

Directly the impact of the required physical nature forms executive (IU). It converts control signals, for example, in the form of a voltage of a constant or pulsed current, in the speed of rotation of the actuator, into the mechanical movement of the valve on the steam line and so on. To perform these transformations, you will need: digital signal converters into analog; electrical signal transducers in non-electrical; amplifying devices, etc. At the same time, as intermediates, digital signal codes may be required, or signal representation form. For example, binary numbers codes in a proportional number of pulses, single-phase signals into multiphase used to control stepper motors, etc.

Under the action of disturbing effects, the object comes out of the normal state (mode), and SAU returns it to the required (normal) mode of operation. The control process proceeds in real time, that is, at a rate determined by the nature of physical processes. If the control exposure is delayed in time or excessive, there may be an unstable operation mode of the system, in which the object coordinates can take unacceptable values \u200b\u200band either the object itself, or the individual system devices will fail the emergency mode. Therefore, in the theory of SAU basic are problems of provision of sustainability and accuracy of management.

Most of the listed transformations can be performed using digital microelectronic devices. Fully digital is the UU when it is based on controlling microevs or on digital chips.

Digital microcircuits are performed digital sensors of physical quantities, as well as partially analog-digital and digital-analog signal converters.

B1.2. Information transmission systems (sleep)

With an increase in the distance between IIU and UU (Fig. B1), as well as between UU and IU, there is a task of transmitting information. The need to transmit information at considerable distances occurs not only in spatially developed automatic control systems and control, but also in systemsothers communication types (telegraph, telephone, telefax, etc.). In addition, the need to transmit information arises in computing systems, data transmission systems, telemechanical systems, etc. This task is complicated by the fact that in the process communication over linesparameters are distorted signals And this, in turn, can lead to distortion of information to a decrease in its loyalty (the probability of its correct reception). The distortion of the signals is due to the action of interferencearising in communication lines. Interference, as a rule, have random nature and in their parameters may not differ from the parameters of the signals. Therefore, they are "able to" distort signals and even "reproduce" information transform the transmitted message. The last most unwanted event in the transmission of information.

To ensure high loyalty and maximum speed ( e.f.fEETING) Information transmission, additional signal transformations are required and special transmission methods.

These transformations include coding and reverse procedure decoding information (and signals). Coding is the procedure for converting a message to a signal. In this case, transformations are carried out according to a certain rulesthe totality of which called code.

Coding information is performed on the transmitting side, and decoding on the reception. Distinguish noise-resistant coding and efficient. purpose noise-resistant coding Build (SFOrmating) signal less subject to interference, give him tbutthe structure to the error occurring in the process of transmission on the reception side could be detected or corrected. And, thus, to ensure high faithfulness of the transfer.

purposeeffective coding provide maximum SC.aboutinformation transmission rate, since its value is largely determined, how long it is obtained. According to this requirement, the encoded message must bear the required amount of information and, at the same time, have a minimum length so that the transfer required for a minimum of time.

Transfer of signals (and information) is carried out by communication channels. Link this is a path (path) of independent transmission of signals from Istoc.nick to the appropriate receiver (recipient) information.Communication channels are formed by technical means of channel-forming equipment and the same as the communication lines are affected by interference.

One of the main solutions in the sleep tasks is the task of creating the required number of communication channels. The efficiency and noise immunity of transmission is largely determined by the communication channels used. Under noise immunity understand the ability of the system (Signal, code) correctly perform your functions in the conditions of interference.

Typically, the same system can be used to transmit information from many sources to the appropriate number of receivers (recipients). Therefore, the formation of the required number of channels with the necessary noise immovability is assigned to the communication device. In this case, the following transformations can be performed in the communication device: modulation and demodulation signals; strengthening transmitted and received from landnII link links; limit by level and frequency spectrumsignals and some others.

Depending on the scope of use (use), there is a need for additional transformations such as converting the shape of signals, their physical nature, the normalization of the parameters of the incoming signals and signals issued by the system to external devices; Temporary storage of communication transmitted to the communication channel and the signals issued.

The listed transformations predetermine the functioning composition of the transmitting and receiving instrument of information transmission systems (Fig.V2).

As can be seen according to the scheme, the transmission is carried out in one direction from left to right. The input and primary information conversion device (UVI) converts signals from sources from sources to unified "primary" signals that cannot be directly transmitted over long distances. Usually, these unified signals are a DC voltage with fixed values \u200b\u200bin terms of level. In the UVV unit, the primary signals are saved at the transfer time (in the buffer storage device), after which they are erased from the memory. The coding device (kU) converts primary signals to encoded signals having a specific structure and format that allows you to transmit them (signals) over long distances ("Telecommus"). As a rule, this device is a combinational, although in some cases can be performed and sequence (multiple). Here are implemented logical and arithmetic operations of coding procedures.

The main purpose of the communication device (Fig. B2) is the creation or organization of communication channels On the link provided. Communication line This is the material environment between the transmitter (PRD) and the receiving system (PRM) of the system. The figure shows a two-wire electrical communication line. However, radiolines and fiber optic communication lines and others can be used. Depending on the type of line in PRD and PRM, various conversion of signals are performed to match their parameters and characteristics with the parameters and characteristics of the communication line and conversion directed to increased noise immunity Signals.

On the reception side, the coded signals received from the communication line are again converted by the decoding device (DCU) into the primary signals. At the same time, the decoding procedures received are detected and errors can be corrected and, thereby ensuring the required loyalty of information transmission. BUT output converters (VP) Converts these primary signals into the form and form (physical nature), which the recipients of information can perceive.

It should be noted that most functional "nodes" and "blocks" shown in Fig.V2 can be performed on digital chips. Therefore, information transmission systems are usually digital.

B1.3. Information processing systems

(Computing Systems)

Listed above typical tasks can be solved and formalized by mathematical and logical methods. In turn, these methods operate with the simplest operations (arithmetic or logical), the fulfillment of some "source data" obtained a new result, previously unknown. This generality of the methods of solving a variety of information processing tasks made it possible to create a separate class of devices and systems whose intended purpose (initially) was automating computational procedures Electronic computing machines (computers). At the present stage of the development of computing equipment, the computer "turned" into computers, on the basis of which modern computer systems of processing and information transfer are being built. A generalized structural diagram of some computing system is shown in Fig.V3.

The processed data is pre-through input device UVV Follow on memory device Zausewhere the processing is saved for all time. In the same memory, the processing program of incoming information is also stored.

The system of system operation in the same way as "data" is stored in a storage device in the form of multi-digit binary numbers recorded in the cells of the zoom at certain addresses (memory cell addresses). Binary numbers whose combination displays the data processing program is structured to a certain number of parts, each of which has a certain purpose. In the simplest case, the following parts are: 1) the operation code that must be performed with two binary numbers displaying "data" values \u200b\u200band called "operands"; 2) the address of the first operand; 3) the address of the second operand. The combination of these parts forms a "command".

The performance of the computer is to serial execution of commands specified by the program. Coordinates the work of all blocks in time and manages them managing device Uu. And directly logical and arithmetic operations (actions) over the operands performs arithmetic logical device Al.which in the signal from the UU "Operation Code" is configured to perform a specific operation.

The control device decrypts the command received from the memory (Fig. B3 "The next command"), the operation code sends to Alu and it is prepared for the appropriate operation. Then forms the operand sample signals (see the "Data Address" signal) and defines the address of the next command to be performed on the next computer's work clock ("Add a Command Address"). Operands are read from the SGA signals from the UU, and Alu performs the necessary actions. In this case, an intermediate result is formed ("the result of the operation"), which also saves the memory. Depending on the result, the operation may need to change the command execution sequence, or stop processing data, or display the error message operator. For this purpose, the "Sign of Result" comes from Alu on the UU. The processing process of entered data (information) continues until the "end of the calculation" command is not retrieved, or the operator does not stop the data processing process at its discretion.

The resulting processing result is also kept in the memory and can be removed through output device Hawmerat the end of the processing process or during the process, if this is provided for by the program.

To "communicate" an operator with a computer provided terminal devices T.intended to enter the command operator and other messages and to display the Operator of the "Messages" from the computer.

Figure. V3 does not show the connection of the control device, providing synchronization of the operation of all components of the computer. A wide arrows displays the ability to parallel data transmission (simultaneous transmission of all discharges of multi-digit binary numbers).

Almost all shown in Fig.V3 blocks (except for terminal devices) can be fully fulfilled only on digital integral chips (IC). In particular, UU, Alu and part of the memory (register memory COP) can be made in the form of a large degree of integration. Named set of blocks forms microprocessor The centercred computer processor made by means of integral technology on one semiconductor crystal.

Input and output devices, as a rule, consist of buffer storage registers that serve for temporary storage, respectively, input and output data and to match the system with external devices.

A storage device (memory) is usually separated into two parts: operational memory (RAM) and constant memory. The first serves to store intermediate calculations, its "content" is constantly changing during data processing. RAM works in reading modes and "records" data. And the second, permanent memory (ROM), serves to store standard subroutines and some systematic (service) subroutines that control the processes on and off the computer. As a rule, the ROM is performed on the user-programmable IC ROM (PPZU), or the ROM (remed-reformed by the User reprogrammed by the User (Remes) are processed in factories. These are usually non-volatile storage devices in which the recorded information is not "destroyed" even when they are disconnected from the power supply.

Alu includes the names of the IC, which perform logical and arithmetic operations with binary numbers, logical elements and a number of other functional nodes that serve to compare the numbers digital comparators to increase the speed of the arithmetic operations performed, for example, "Accelerated Transfer Blocks", etc.

The Wu includes timer devices that set the clock frequency of the system and, ultimately, defining its performance, command codes, programmable logical matrices, registers, microprogram control units, as well as "ports" of I / O ports.

All listed function nodes are performed as integral digital devices.

The main problems Computing systems are, firstly, raising them performance (speed). And, secondly, ensuring the operation of systems in a real "scale" time.

The first problem is a system-wide character and is solved by applying a new element base and special methods of information processing.

The second problem occurs when using computing systems for managing production processes and is that the velocities of the flow of production and computing processes must be coordinated. Indeed, the functioning of the computing system (Sun) occurs in the so-called "machine" time, when a certain fixed and indivisible time interval is taken per unit of time, called "Takt of work" of a computer or computer, while real physical processes, such as technological processes, proceed to Real time, measured in seconds, fractions of a second, in hours, etc. In order for the use of the computer to be possible, the speed of processing information is necessary to make no less velocity of the actual physical processes. The solution to this problem is achieved by the organization of special information exchange methods (data) by the control computer with peripheral devices and the use of special, so-called interfacecaps and devices. The function of interface schemes includes:

determining the address of the external device that requires the exchange of information with the processor or with a storage device of the system;

formation of the operation of the interruption of the operation of the Sun processor and initializing the transition to the object of service of the object requested the interrupt. This is carried out by special prioritization system;

implementation of queues for serving external devices;

approval by parameters and time of exchange signals, etc.

Thanks to modern achievements in the field of integral technology in the manufacture of microelectronic devices, the creation of microevm and computers characterized by small dimensions, low energy consumption and acceptable cost, has become possible to use them as part of various destination systems. At the same time, these systems acquire new qualities and become multifunctional with the possibility of a flexible transition from one mode of operation to another way of changing the system configuration. In turn, these advantages reveal new perspectives in the use of computer systems in a wide variety of areas of human activity: in science, in medicine, education and training and especially in the technique.

For example, a telephone connection was traditionally carried out by analog devices when the human speech was transmitted (by wire) signals as variable audio frequency currents. Now there is an intensive transition to a digital telephone connection, in which the analog signals (from the microphone) are converted into digital, transmitted over long distances without significant distortion. On the reception side, these digital signals are converted to analog and brought to the phone. The transition to digital communication allows you to improve the quality of speech transmission, in addition, the telephone network can be used for other services: security alarm; fire alarm; For conference calls of several subscribers and so on.

AT 2. Comparative evaluation of digital and analog devices

microelectronic technology

Recommending the issue of building or designing, any device, should be pre-decide on the direction of design, how will the device be? Analogor discrete (digital)? In turn, this decision can be taken, knowing the advantages and disadvantages of those and other devices. Pre-give the definitions of "analog" and "digital" devices.

Analogcalled such device, in which all signals are input, output and intermediate (internal) are continuous, are described by continuous mathematical functions. These signals are characterized by an infinite set of values \u200b\u200bin terms of (states) and are continuous in time, although the range of changes in the continuous signal values \u200b\u200bis limited. Therefore, sometimes such devices are called arrangementj.n.e.included.

Discrete devices or devices discrete action Call those who have input, output and intermediate signals are characterized by a countable set of values \u200b\u200bin terms of level and existence at certain time intervals. Such signals can be displayed in a particular positioning system (corresponding numbers). For example, in a decimal number system or a binary number system. The binary representation of the signals has found the greatest application in the technique and in formal logic when specifying statements and when displaying conclusions from several parcels. Therefore, discrete devices are called logical (by analogy with formal binary logic) or digital, taking into account the possibility of describing them using the numbers of the positioning system.

Disadvantages of technical means of analog equipment

The presence of "drift" and "noise". Drifting This is a slow change in the signal due to the discrete nature of phenomena, relative to the value given. For example, for electrical signals, the discrete nature of the electric current flows is caused by electrons and "holes", which are carriers of electrical charges. Noise These are random changes of the signal caused by external or internal factors, such as temperature, pressure, the voltage of the magnetic field of the Earth, etc.

Methodological difficulties in determining the concepts of "equality zero" and "equality of analog signals". And as a result, the existence of the problem of "providing a given accuracy (error)" transformations and signal transmission.

The possibility of the emergence of unstable operation modes and the existence of the problem of "sustainability" of the operation of systems and devices. An unstable mode is characterized by occurrence in the device or system of non-unforgetious oscillations in changing some signals. In electronics, this phenomenon is widely used when constructing pulse generators and harmonic oscillation generators.

Technical difficulties in the implementation of storage devices and device temporary delay of analog signals.

Insufficient level of integration of analog elements and their versatility.

Comparatively small range of analog signal transmission due to energy scattering in communication lines.

Relatively large energy consumption, as the analog elements operate in linear sections of their transient characteristics and "consume" energy in the initial (source) states.

Advantages of technical means of analog equipment

The adequacy of the display of physical processes and patterns: both are described by continuous dependencies. This allows you to significantly simplify the fundamental technical solutions of analog devices and systems.

Operation and simplicity of changes in operation modes: It is often enough to change the resistance of the resistor or the capacitor capacity so that the unstable mode is changed to the steady or provide the specified transition process in the device.

No need to convert analog values \u200b\u200binto discrete. These transformations are accompanied by error and a certain spending time.

Advantages of technical means of digital equipment

The possibility of software management, which increases the flexibility of changing the structure and algorithm of system functioning, makes it possible to simplify the implementation of adaptive management laws.

Easy to ensure a given reliability, accuracy and noise immunity of systems.

Easy to ensure the compatibility of devices with information processing devices in digital form (computer, computers).

High degree of constructive and functional integration, versatility with the possibility of building systems according to typical design solutions. In turn, it makes it possible to reduce the cost of production and operation of systems and devices.

The ability to design formal logical methods, which reduces the design time of the devices and makes it possible to change the functions of devices (and systems based on them) by the methods of aggregate construction during operation.

Disadvantages of technical digital equipment

The need to convert analog signals to discrete. These transformations are accompanied by the appearance of error and time delays.

The relative complexity of changing modes of operation. To do this, it is necessary to change the structure of the system or the algorithm of its functioning.

The complexity of the process analysis of systems, both when checking the correctness of their operation and when searching for emerging faults. Digital devices are characterized by a large functional complexity, which requires special "diagnostic" devices that are studied in a special field of technology, called technical D.andagnostandkoya.

Increased requirements for the culture of production and to the culture of technical means of digital equipment. In turn, it stimulates the need to improve the qualifications of the service personnel and requires high qualifications from it.

A comparative analysis of the listed advantages and deficiencies gives conclusion in favor technical means digital technology. Therefore, currently digital devices are widely implemented, it would seem, in traditional areas of analog technology: television, telephone, in recording technique, radio engineering, in automatic control systems and regulation.

1. Basics of microelectronic technology

1.1. Basic concepts and definitions

Microelectronics The main direction of electronics, which studies the problems of design, research, creating and applying electronic devices with a high degree functional and constructinnoah integration.

Microelectronic productimplemented by means of integrated technology and performing a specific function for conversion and signal processing is called integral microcham (IS) or just integrated circuit (IP).

Microelectronic device A combination of interrelated IP that performs the completed enough complex function (or several functions) on processing and conversion of signals. The microelectronic device can be constructively decorated in the form of a single chip either on several ISS.

Under functional integration Understand the increase in the number of functions implemented (executed) by some features. In this case, the device is considered as single wholeindivisible. BUT constructive int.e.grace This increase in the number of components in the device is considered as single whole. An example of a microelectronic device with a high degree of constructive and functional integration is microprocessor(See above), which, as a rule, is performed in the form of one "big" IC.

Circuitry is part of microelectronics whose subject is construction methods Devices for various purposes on micraboutwide application schemes. The subject of the same digital circuitry are methods for constructing (designing) devices only on digital IS.

Feature of digital circuit equipment Is wide application to describe device functioning processes formal or formally natural languages and based on them formalized design methods. Formal languages \u200b\u200bare boolean algebra (Logic algebra, Bul algebra) and the language of "automatic" logical functions algebra of states and events. Thanks to the use of formalized methods, achieved multivariate In solving applied tasks, the possibility of optimal selection of circuit solutionsfor one or another criteria.

Formal methods Characterized by a high level of abstraction of distraction, disregard by the private properties of the described object. The attention is focused only on general laws in mutual relations between the components of the object with its components. Such "patterns", for example, includes rules for arithmetic action in the algebra of numbers (the rules of addition, subtraction, multiplication, divisions). At the same time, they are distracted from the meaning of numbers (whether it is apples or tables, etc.). These rules are strictly formalized, formalized and the rules for obtaining complex arithmetic expressions, as well as procedures for calculating such expressions. In such cases, they say formal and s.n.tAtosIS. and grammar Language Descriptions.

In formal-natural languages, the syntax is formalized, and the grammar (rules for constructing complex expressions) obeys the grammar of the natural language, such as Russian or English. Examples of such languages \u200b\u200bare various tabular languages \u200b\u200bof the description. In particular, the theoretical database of the description of digital devices is the "theory of finite automata" or "theory of relay devices and finite automata".

1.2. Classification of microelectronic devices

All varieties of microelectronic devices (MEU) can be classified according to various features:

on the principle and nature of the action;

on functional purpose and functions performed;

according to manufacturing technology;

in terms of application;

according to constructive execution and technical characteristics and so on.

Consider now in more detail the separation of the MEA on classification features.

According to principle (character) actions All MEAs are divided into analog and digital. The concepts of analog and discrete devices have already been given above and, including digital. Here, note, if in discrete devices, all signals take only two conditional values \u200b\u200bof logical zero (log.0) and logical unit (log.1), then the devices are called logical. As a rule, all digital devices relate to logical devices.

Depending on the functions (functional purposes), the following microelectronic devices distinguish:

I. Analog

1.1. Amplifying devices (amplifiers).

1.2. Functional converters performing mathematical operations with analog signals (for example, integration, differentiation, etc.).

1.3. Measuring transducers and sensors of physical quantities.

1.4. Modulators and demodulators, filters, mixers and harmonic oscillation generators.

1.5. Storage devices.

1.6. Strength stabilizers and currents.

1.7. Special integral microcircuits (for example, for processing radio and video signals, comparators, switches, etc.).

II. Digital Maou

2.1. Logic elements.

2.2. Encodes, codes decryptors and coderers.

2.3. Storage elements (triggers).

2.4. Storage devices (RAM, ROM, PPZ, SLM, etc.).

2.5. Arithmetic logic devices.

2.6. Selectors, shaders and impulse generators.

2.7. Accounts (pulse counters).

2.8. Digital comparators, discrete signals.

2.9. Registers.

2.10. Special purpose microcircuits (for example, timer, microprocessor IP microprocessors, etc.).

The given classification is far from comprehensive, but it allows us to conclude that the nomenclature of digital devices is much wider than the nomenclature of the analog MEA.

In addition to those listed, there are microcircuits of signal levels converters, such as Schmit triggers, in which the input signals are analog, and the output discrete, binary. Such microcircuits occupy an intermediate position. Similarly, the chips of the analog-digital and digital-analog converters (ADC and DAC), the switches of analog signals controlled by discrete signals should be attributed to the "intermediate" MEU.

Depending on the number of functions implemented, distinguishes oNNaboutfunctional (simple) and multifunctional (Complex) MEA. In multifunctional devices, functions can be performed. at the same time or sequence in time. Depending on this, in the first case, the devices are called "parallel" devices, and in the second case, sequential operation devices or "sequence". If the setting of a multifunction device for performing a particular function is carried out by switching the inputs (physical memory of the electrical circuits), then such a device is called the device with " hard logic»Work. And if the change in the functions performed is performed using additional external signals (on the so-called control inputs), then such an MEU should be attributed to "software-managed". For example, an arithmetic and logic devices (ALU) might implement arithmetic or logic operations with two multi-digit binary numbers. And the setting to perform arithmetic (or logical) operations is carried out by one additional external signal, depending on which the desired actions will be performed. Therefore, Alu should be attributed to a software-managed MEA.

According to manufacturing technology All ISs are divided into:

Semiconductor;

Film;

Hybrid.

IN semiconductor IC All components and compounds are made in the volume and on the surface of the semiconductor crystal. These IS are divided into b.andpolar chips (with a fixed polarity of the supply voltage) and on unipolar With the ability to change the polarity of the supply voltage. Depending on the circuitry of the "internal content", bipolar microcircuits are divided into the following types:

TTL transistor-transistor logic;

TTLSH transistor transistor logic with transistors and spear diodes;

ESL Emittern and linked logic;

And 2 liters of injection logic and others.

The chips of unipolar technology are performed on TIR transistors ("metal-dielectric-semiconductor"), or on MOS-transistors ("metal-oxide-semiconductor"), or on CMOS transistors (complimentary "metal - oxide - semiconductor").

IN plenches IP All components and connections are performed only on the surface of the semiconductor crystal. Distinguish talkless(with a layer thickness of less than 1 micron) and tolstoplaney With a thick film of more micron. Tonclosure IPs are manufactured by the thermal pumping and cathode spraying method, and the thick-dollarmed silk-screening method with the subsequent ignition of additives.

Hybrid IP consists of "simple" and "complex" components located on one substrate. As complex components, semiconductor or film IP crystals are commonly used. Simples include discrete components of electronic technology (transistors, diodes, capacitors, inductance, etc.). All of these components are structurally located on one substrate and electrical connections are also performed on it. Moreover, one substrate with components located on it form one "layer" of hybrid IP. Distinguish single-layer and multi-layered Hybrid IP. Multilayer hybrid IP is capable of performing enough complex signals processing functions. Such a microcircuit is equivalent on the action of "microblocked" devices, or if it is intended for self-use, the action of a "whole" block.

In addition, any chips are estimated quantitative showbuttelem them difficulties. As such an indicator used " power integration» k., equal to decimal logarithm from total N. components placed on one semiconductor crystal, that is

k. = lQ. N.. (1)

In accordance with the formula (1), all chips are divided into microcircuits of the 1st, 2nd, third, and so on the degrees of integration. The degree of integration only indirectly characterizes the complexity of microcircuits, since it is taken into account only constructiveintegration. In fact, the complexity of the chip depends on the number of mutual relations between the components.

In engineering practice, the quality characteristic of the complexity of chips in the concepts of "small", "medium", "big" and "super-large" IP is used.

Table 1.1 provides information on the mutual compliance of high-quality and quantitative measures of the complexity of IP by their species.

Table 1.1.

From the analysis of Table 1.1, it follows that, in comparison with digital use, analog chips with the same degrees of integration in their composition (on a semiconductor crystal) more than three times, a smaller number of components. This is explained by the fact that the active components (transistors) of the analog microcircuit work in linear mode and larger energy dissipate. The need to remove heat released during energy scattering limits the number of components placed on one crystal. In digital chips, active ingredients operate in key (transistors or locked, or open and are in saturation mode). In this case, the dissipated power is insignificant, and the amount of heat released is also slightly and therefore the number of components on the crystal can be placed more. (Crystal dimensions are standardized and limited.) With unipolar technology, the crystal volume occupied by the field transistor is approximately three times less than the volume occupied by the bipolar transistor ( n.- p.- n. or p.- n.- p. type). This explains the fact that active ingredients on a standard size crystal in a unipolar microcircuit can be placed more.

By constructive execution Depending on the functional complexity, microelectronic devices are divided:

on simple chips (ISS);

on microspectors;

on microblocks.

Im. microelectronic product manufactured in unified Tekhnol.aboutgycical cyclesuitable for self-use or as part of more complex products (including microsives and microblocks). Microcircuits may be inapproprous and have an individual body that protects the crystal from external influences.

Microsoft A microelectronic product that performs a sufficiently complex function (function) and consisting of electrical particulate components and microcircuits manufactured in order to miniature radio-electronic equipment. Essentially, hybrid chips are microchrokes. The simplest microscope can be, for example, a set of microresistors made on a semiconductor crystal and decorated in a single housing (as a chip).

Microblock It is also a microelectronic product, consists of electrical α-components and integrated circuits and performs a complex function (function).

As a rule, microspects and microblocks are manufactured in various technological cycles, and maybe at different manufacturer plants.

As classification technical characteristics commonly used power consumption (one microcham) and fightj.corollary.

By power consumption All IS can be divided into: but) micraboutpowerful (less than 10. mW.); b.) low power (no more than 100 mW.); in) middle power (up to 500 mW.) I. g.) powerful (more or \u003d 0.5 T.).

By speed (Maximum delays in the time of distribution of signals through IP) chips are divided into: but) Ultra-fast with boundary frequency f. GR switching over 100 MHTS; b.) high-speed ( f. gr from 50. MHTS up to 100. MHTS); in) normal speed ( f. GR from 10. MHTS up to 50 MHTS). At the same time, the distribution delays are about the units of nanoseconds (10 -9 from.) to 0.1 microseconds (1s \u003d 10 -6 from.).

Digital microelectronic devices, including chips and others discrete Devices, conveniently classified by h. but rastera addiction output signals from the input. As is customary in the theory of finite automata. In accordance with this feature, all devices are made to divide on combinational and sequence.

IN combinational devices The values \u200b\u200bof the output signals at some point in time are uniquely determined by the input signals at the same time. Therefore, we can assume that the operation of such devices does not depend on time. They are also called devices "without memory», dispense Devices or devices of one-stroke action. In the theory of finite automata, combinational devices are called "primitive finite automata."

IN sequence devices The values \u200b\u200bof the output signals (output signals) depend on the input signals values \u200b\u200bnot only during the time in the current time, but also from the input signals in the previous points in time. Therefore, such devices are called devices with " memory», multiple devices, and in the theory of finite automata, just? eltimate machine gun (not trivial).

When considering educational material, in the future, for basic Let's take this particular classification, as construction methods (synthesis) and the functioning processes of these devices significantly differentbuteat.

Finishing the presentation of classification issues, we note that the above list of classification features and a list of microelectronic products (chip) is far from exhaustive. In the future, as needed, we will add this list.

1.3. Logic elements

Logic elements Refer to the simplest combinational "devices" having one output and one or two inputs. They received their name for the reason that their functioning can be fully described logical functions And in particular, Boolean functions.

As in formal logic, all statements can be true or false and logical functions can take only two conditional values: a logical unit (log.1) "Truth" and logical zero (log.0) "Lies".

When describing the work of logical elements output signals put in unambiguous compliance functions, but input signals arguments These functions. Thus, both functions, and function arguments, as well as input and output signals of logical elements are binary. If you neglect the actual transition time of the logical element from one state (status of log.1) to another (the status of the log.0), then no arguments and no functions will depend on the time-time factor. Rules for obtaining and transformation of logical expressions consider algebra logic or boulevalgebra.

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"Digital circuit engineering"

Kharkov 2006.

Preface

1 logical and circuit breeds of digital microcircuit

1.2 Logic elements

1.3 Basic Laws Logic Algebra

1.4 disjunctive normal forms

1.5 Minimization of logical functions

1.6 Synthesis of combinational logic schemes

2 Combination diagrams

2.1 Basic provisions

2.2 Decifrators

2.3 Encifers

2.4 Demultiplexors

2.5 Multiplexers

2.6 Arithmetic devices

3 trigger devices

3.1 Basic concepts

3.2 Asynchronous RS Trigger

3.3 Synchronous triggers

4 Registers

4.1 General Registers

4.2 Memory registers

4.3 Shifting registers

4.4 Reversing registers

4.5 Universal Registers

5 counters

5.1 General information about counters

5.2 Meters with consistent transfer

5.3 Parallel Transfer Counters

5.4 Reversible counters

5.5 Counters with an arbitrary account ratio of not 2N

List of literary list

Preface

This methodological manual contains information that provides a study of disciplines:

- "Digital circuitry" for students of the specialty 5.091504 (maintenance of computer and intelligent systems and networks);

- "Microchemistry" for students of the specialty 5.090805 (design, production and maintenance of products of electronic equipment);

- "Electronic devices and microelectronics" for students of the specialty 5.090704 (design, production and maintenance of radio engineering devices).

The material that is presented in this work is intended to familiarize students with the basics of modern digital microcircuit equipment and includes the main types of digital devices that are widely used as independent products in the form of small and medium integration chips, and as part of a highly integration chip: microprocessors and microcircuits. microcontrollers.

The methodological manual consists of five sections:

Logical and circuit breeds of digital microcircuit equipment,

Combination circuits,

Trigger devices

Registers

Counters.

The exposition of the material is constructed in such a way that consistently "from the simple to complex" present the main theoretical principles of the analysis and synthesis of digital devices. Each section contains subsections in which information on the conditional graphic designation of the studied device is given, its functioning table, a functional or schematic diagram and temporary work charts where it is required is given. Each of the circuits are given a detailed description of the logic of its work with such a calculation so that each student item has mastered the principles for analyzing the operation of digital circuits and acquired the necessary skills. Each of the shown schemes is typical for this device. In this case, the other circuit implementation is not excluded.

The main concepts, definitions, the rules are highlighted by the "bold" font to make the placement of the subject more convenient and visual.

Considering that the exposition of the material is carried out in ascending order of the complexity of the digital devices studied and at the same time each subsequent theme is based on the material of the previous one, it is advisable to use this methodological manual in the sequence in which the relevant sections are located.

This manual is useful to use not only when studying the theoretical foundations of digital microcircuit equipment, but also in preparing for laboratory work, the purpose of which is to deepen the knowledge and acquire practical skills to assemble and debug digital devices. The manual can be used to independently study, as well as for courses and thesis design.

1 logical and circuit breeds of digital microcircuit

1.1 Basic Logic Algebra Concepts

Logic is a science of laws and forms of thinking.

Mathematical logic - science on the use of mathematical methods to solve logical tasks.

All digital computing devices are built on elements that perform certain logical operations. Some elements provide the processing of binary characters representing digital or other information, others - switching channels for which information is transmitted, finally, third - control, activating various actions and implementing the conditions for their execution.

The electrical signals acting on the inputs and outputs of the named elements have, as a rule, two different levels and, therefore, can be represented by binary symbols, for example 1 or 0. We will consider signifying the accomplishment of any event (for example, the presence of a high voltage level in which -Lo point of the scheme) symbol 1. This symbol is called a logical unit. The absence of any event is denoted by a symbol 0 called a logical zero.

Thus, each signal at the input or output of the binary element is complied with a logic variable that can only receive two values: the state of the logical unit (the event is true) and the state of the logical zero (the event is false). These variables are called Boolean named English Mathematics J. Bul, who still developed the main provisions of mathematical logic in the nineteenth century. Denote the logical variable symbol x.

Various logical variables can be associated with functional dependencies. For example, the expression y \u003d f (x1, x2) indicates the functional dependence of the logical variable from the logical variables x1 and x2, called arguments or input variables.

Any logical function can always be represented as a set of simple logical operations. These operations include:

Denial (operation "not");

Logical multiplication (conjunction, operation "and");

Logical addition (disjunction, operation "or").

The denial (Operation "Not") is such a logical connection between the input logic variable x and the output logic variable in which it is true only when X is false, and, on the contrary, is falsely only when true x. I will depict this functional dependence in the form of table 1.1, which is called the truth table.

The truth table is a table that displays the correspondence of all possible combinations of binary arguments values \u200b\u200bof the logical function values.

Table 1.1- Tatt of the truth of the operation "not"

The logical function is not a variable from written as y \u003d

Logical multiplication (conjunction, operation "and") is such a function that is true only when all multiply variables are true at the same time. The truth table of the logical multiplication operation corresponds to Table 1.2.

Table 1.2- Timing Title Operation of Logical Multiplication

Operation "And" is denoted by the point (). Sometimes the point is meant. For example, the operation "and" between two variables x1 and x2 is denoted as y \u003d x1 x2.

Logical addition (disjunction, Operation "or") is such a function that is false only when all the terms of the variables are simultaneously false. The truth table of the logical addition operation corresponds to Table 1.3. Operation "or" is indicated by the sign V. For example, y \u003d x1 v x2.

Table 1.3 - Table of Truck Operation of Logical Addition