Study of the logic of work. logical elements. Study of typical logical elements Study of the operation of logical elements
This set allows you to study the logic of operation of the main types logic elements. The set is placed in a package consisting of a black plastic box measuring 200 x 170 x 100 mm
The stack contains four modules of standard size 155 x 95 x 30 mm. In addition, there should be connecting wires, but in the copy with which the author dealt, they were missing, but the instruction manual was preserved.
AND gate
The first module is a logical element AND, a signal appears at its output only if the signal arrives at both of its information inputs.
The standard module is printed circuit board, which is closed on top with a transparent plastic cover secured with two screws.
The module is easily disassembled, which allows you to examine the device's printed circuit board in detail. On the back side, the printed conductors are covered with an opaque plastic cover.
OR gate
The logic element is arranged almost similarly OR, a signal appears at its output provided that a signal arrives at any of its information inputs.
NOT gate
Logic element NOT. The signals at the input and output of this element always have opposite values.
Trigger
Trigger- a logical device with two stable states, used as the basis for all kinds of devices requiring information storage.
Generally this set in terms of digital electronics, it is similar to the “Electronic Amplifier” kit. Of course, the variant of implementation of logical elements presented in the set is far from the only one. In fact, logical elements are implemented here as they were done in the 60s of the 20th century. In this case, the important thing is that when working with this set, you can directly study the simplest circuit example that lies at the very basis of digital semiconductor electronics. Thus, a separate logical element ceases to be a “black box” that works on pure magic. Highly visible and protected at the same time electrical diagram, this is just what you need to learn the basics of electronics. Review author - Denev.
Transcript
1 16 Study of the logic of operation of logical elements Purpose of the work The purpose of the work is to consolidate knowledge of the fundamentals of logic algebra and gain skills in the study of logical elements and connecting them into the simplest combinational circuits.
2 17 to 1. Information from theory combinational circuits consist of logical elements. A logic element is the simplest part of a digital circuit that performs logical operations on logical variables. When using integrated circuits, such elements are usually NAND, NOR, AND-NOR elements. The operation of logical elements is described by truth tables. On electrical functional diagrams, logical elements are displayed in the form of conventional graphic symbols (CGI). Conditional graphic symbols Logic elements for two inputs are shown in Fig. 2.1a 2.1e. The truth tables for these elements have the form shown in table NOT 2I 2OR 2I-NOT 1 1 a) b) c) d) e) Fig. Graphic symbols of logical elements Table 2.1 Truth table of logical elements Inputs Type element a b NOT 2AND 2OR 2AND-NOT 2OR-NOT Y = a Y = ab Y = a v b Y = ab Y = a v b To write a logical function in SDNF (perfect disjunctive normal form) according to the truth table it is necessary for each rows of the table in which the function Y takes the value “1”, write down the logical product (conjunction) of the input variables (for Table 2.1 we mean variables a and b). Moreover, if the variable in this line takes the value “0”, then in the conjunction it is written with inversion. Next, if necessary, you should minimize the resulting function.
3 18 2. Short description laboratory installation A stand type UM-11 is used as a laboratory installation. The stand is based on a power supply, clock and single pulse generators, a set of logical elements and triggers, as well as indication and control elements. The inputs and outputs of all elements are displayed on the front panel of the stand in the form of contact sockets. On the front panel of the stand there are conventional graphic symbols of logical elements and triggers. Using special wires with lugs, you can connect elements to each other, supply signals from generators or switches to the inputs of elements, and also observe signal values using indicator lights or using an oscilloscope. A fragment of the front panel of the stand is shown in Fig. Fig. A fragment of the panel of the UM-11 stand In addition to the elements for 2, 3 and 4 inputs shown in Fig. 2.2, on the front panel there is also an AND-NOT element for 8 inputs. This set of elements corresponds to a series of 155 integrated circuits. Thus, using the stand, you can assemble combinational circuits and check the correctness of their operation.
4 19 3. Order of work Task 1. Investigate the logic of the operation of the 2I-NOT element. To do this, assemble on a bench the circuit shown in Fig. When constructing the circuit, use switches with which you can apply “0” and “1” signals to the input of the element. Observe the output signals by the state of the indicator light. When assembling the circuit, you should pay attention to the fact that each switch can set the value of one variable. In this case, the switch has two outputs: direct (upper) and inverse (lower). So from the upper output of the switch you can get the direct value of the variable, and from the lower output the inverse value (Fig. 2.3). The direct value of the variable itself depends on the position of the switch: in the upper position of the switch the variable is equal to “1”, in the lower position “0”. Accordingly, the inverse value will be the opposite. Using switches, apply all combinations of signals “a” and “b” to the input of the circuit and enter the resulting values of the output signals into the truth table. Compare the resulting table with the data in table. 2.1. for the 2I-NOT element. Include in the report: the assembled circuit, the UGO of the 2I-NOT element and the resulting truth table. +5V a 1 a b Y 1 b Fig Scheme for studying the 2I-NOT element Task 2. Investigate the logic of the operation of the 3I-NOT element. To do this, assemble a circuit similar to the circuit in Fig. Check the logic of the circuit for different values of input signals and create a truth table. Task 3. Investigate the logic of operation of the NOT element, implemented on the basis of the 2I-NOT element. To do this, assemble the circuit shown in Fig. 2.4. and complete it with a switch and an indicator light. Fig Implementation of a NOT circuit using 2I-NOT elements
5 20 Check the logic of the circuit operation at different values of the input signal and compare it with the data in table. 2.1 for the NOT element. Task 4. Assemble the circuit shown in Fig. 2.5, and explore the logic of its operation. Create a truth table and compare it with the data in the table. 2.1 for element 2I. Fig. Scheme of implementation of the AND circuit using NAND elements. Task 5. Assemble the circuit shown in Fig. 2.6 and examine the logic of its operation. Create a truth table and compare it with the data in the table. 2.1 for element 2OR. Fig. Scheme of implementation of an OR circuit using NAND elements. Task 6. Assemble the circuit shown in Fig. 2.7, and explore the logic of its operation. Create a truth table and compare it with the truth table for the 2I-2OR element. Fig. Example of a diagram using NAND elements 4. Contents of the report 1. Topic, purpose of the work, 2. Results of completing tasks. For each task, provide the experimental design, the UGO of the element under study and the truth table. 3. Analysis of the results obtained. 4. Conclusions on the work.
6 21 5. Test questions 1. What is a logical function? 2. What is a logical element? 3. Explain the logic behind the operation of the NOT element. 4. Explain the logic of the AND element. 5. Explain the logic of the OR element. 6. Explain the logic behind the operation of the AND-NOT element. 7. Explain the logic behind the operation of the OR-NOT element. 8. What is a truth table? 9. How to write a logical function in SDNF using a truth table? 10. How to construct a NOT circuit from AND-NOT elements? 11. How to construct an AND circuit from AND-NOT elements? 12. How to construct an OR circuit from AND-NOT elements? 13. What function does the circuit shown in Fig. implement? 2.7.
23 1. General information about combinational circuits Combinational circuits consist of logical elements. When using integrated circuits, such elements are usually NAND, NOR,
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Laboratory work No. 2
1. PURPOSE OF THE WORK
Study of the functioning of typical logical elements; implementation of basic and other functions using basic AND-NOT and OR-NOT elements; the use of logical elements as signal switches.
2. THEORETICAL PROVISIONS
ICs of the LA type perform the logical function mAND - NOT, ICs of the LE type perform the logical function mOR - NOT (m is the number of inputs), and ICs of the LN type perform the logical function NOT. One package of the LAZ microcircuit contains four 2I-NOT logic elements. One package of the LE1 microcircuit contains four 2OR-NOT logic elements. One package of the LN1 microcircuit contains six logical NOT elements (inverters). The LN1 microcircuit has a push-pull output stage. The symbols and pinouts of the LAZ, LE1 and LN1 microcircuits are shown in Fig. 1.
Picture 1
Logic elements are also called gates (signal switches). This is because they can delay or miss digital information on the principle of a conventional valve designed to control the flow of liquid. The symbol for the 2I valve with the signals at its inputs and output and the timing diagrams of its operation as a switch are shown in Fig. 2.
Figure 2
If rectangular pulses from the generator are applied to the upper input of the 2I logical element, and a logical unit level is applied to the lower input, then the pulses from the generator will pass to the output of the 2I logical element (Fig. 2). This follows from the law of operation of the AND element. If the logical one at the lower input is replaced by a logical zero, then pulses from the upper input to the output of the logical element 2I will not pass, since at least one zero at the input of this element gives a zero at the output.
3. EQUIPMENT
The TsS-02 stand is used as measuring equipment.
4. PROCEDURE FOR PERFORMANCE OF THE WORK
In your work, use the K155JIA3, K155LE1, K155LN1 microcircuits.
1. Study of the functioning of logical elements 2AND-NOT, 2OR-NOT and NOT
1.1. Draw diagrams for studying logical elements (see Fig. 3 a - c). Put on them the numbers of the pins of the selected elements of the microcircuits. Select the LU sources that you will use and put their numbers on the diagram.
1.2. Assemble the circuits shown in these figures one by one.
1.3. By changing combinations of input signals, monitor the output state of the logic element under study with an LED indicator or an oscilloscope. Fill in the truth tables of the elements (Table 1).
Table 1
| A | IN | LA3 | LE1 | LN1 |
| Function |
1.4. Make sure the logic elements are functioning correctly.
Figure 3
2. Implementation of basic functions on basic NAND elements
2.1. Draw the diagrams shown in Fig. 4,a, 4,c. Put on them the numbers of the pins of the selected elements of the microcircuits. Select the LU sources that you will use and put their numbers on the diagram.
Figure 4
2.2.Assemble the circuits shown in these figures one by one.
2.3.When changing combinations of input signals, monitor the state of the outputs of all logical elements of the circuits with LED indicators or an oscilloscope. Create truth tables for the circuits under study.
2.4. Make sure that the results obtained are correct by theoretically analyzing the operation of the circuits under study.
2.5.Using the obtained truth tables, determine the type of function that each circuit performs and write the name of the function in the “type of function” column of the tables.
3. Implementation of basic functions on basic OR-NOT elements
3.1. Draw the diagrams shown in Fig. 5, a, b, c. Put on them the numbers of the pins of the selected elements of the microcircuits. Select the LU sources that you will use and put their numbers on the diagram.
Figure 5.
3.2. Assemble the circuits shown in these figures one by one.
3.3. By changing combinations of input signals, monitor the state of the outputs of all logical elements of the circuits with LED indicators or an oscilloscope. Fill in the truth tables of the circuits under study, similar to the table. 3...5.
3.4. Make sure the results obtained are correct by theoretically analyzing the operation of the circuits under study.
3.5. Using truth tables, determine the type of function that each circuit performs and write the name of the function in the “type of function” column of the tables.
4. Implementation of functions of various types on basic elements AND-NOT and OR-NOT
4.1. Draw the diagrams shown in Fig. 6, a, b. Put on them the numbers of the pins of the selected elements of the microcircuits. Select the LU sources that you will use and put their numbers on the diagram.
Figure 6
4.2. Assemble the circuits shown in these figures one by one.
4.3. By changing combinations of input signals, monitor the state of the outputs of all logical elements of the circuits with LED indicators or an oscilloscope. Fill in the truth tables of the circuits under study.
4.4. Make sure the results obtained are correct by theoretically analyzing the operation of the circuits under study.
5. Application of logic elements as signal switches
5.1. Draw circuits for studying logical elements (see Fig. 7, a - d). Put on them the numbers of the pins of the logical elements of the microcircuits selected for research. Select the LU sources that you will use and put their numbers on the diagram.
5.2. Assemble one by one the circuits shown in Fig. 7, a, c, if there are only LED indicators to control input and output signals. If you have an oscilloscope, assemble the circuits shown in Fig. 7, c, d.
5.3. Observe the waveform at input A of the logic gates and output signal C, first when there is a logical one at input B, and then when there is a logical zero. To do this, connect an LED indicator to the output of the circuits (Fig. 7, a, c). When studying circuits (Fig. 7, c, d), connect the input of the first channel of the oscilloscope to the input A of the logical element, and the input of the second channel to the output of the logical element. Synchronize the oscilloscope sweep with the signal of the first channel. Draw timing diagrams (oscillograms) of the signals at the inputs and outputs of the elements under study for both cases (Fig. 8 a, b).
5.4. Verify the correct functioning of logic elements as signal switches by theoretically analyzing their operation.
Figure 7
Figure 8
The work report must contain:
Title of the work and purpose of the work;
Schemes under study;
Truth tables;
Timing diagrams;
Comparison of experimental data with the results of theoretical analysis;
Conclusions from the work.
CONTROL QUESTIONS
1. How many different combinations are there for the four input signals?
2. What it looks like symbol logical element ZILI?
3. How will the output function of a NAND gate change if its inputs are inverted?
4. Which logic gates invert input signals when passing them to the output?
5. What signals must be supplied to the other two inputs of the ZILI logic element so that pulses from the first input pass to the output?
E.N. Malysheva
Basics
Microelectronics
Laboratory workshop
Tobolsk - 2012
UDC 621.3.049.77
Published by decision of the Department of Technology and Technical Disciplines of the TSPI named after. DI. Mendeleev
Malysheva E.N. Fundamentals of microelectronics. Laboratory workshop: Textbook. – Tobolsk: TGPI named after. DI. Mendeleeva, 2012. – 60 p.
Reviewer: Novoselov V.I., Ph.D. Sc., Associate Professor, Department of Physics and MPF
© Malysheva E.N., 2012
© TGPI named after. DI. Mendeleeva, 2012
Explanatory note
Given tutorial made in the form of a workbook and is offered to accompany a laboratory workshop for students of pedagogical universities studying the fundamentals of microelectronics. The laboratory workshop is conducted using a universal stand and is devoted to the study of elements, components and devices of digital technology.
1. Study of the operation of basic logical elements.
2. Study of the operation of triggers.
3. Study of the operation of registers.
4. Study of the operation of combinational code converters.
5. Study of the operation of meters.
6. Study of the operation of the adder.
7. Study of the operation of an arithmetic-logical device.
8. Study of the operation of a random access memory device.
9. Study of the operation of a computer model.
Each work includes the following sections:
Theoretical material, the mastery of which is necessary to complete the work;
Description of work;
Questions for the test of this work.
Laboratory work No. 1.
Study of the operation of basic logical elements
Goal of the work: study of operating principles and experimental study of the operation of logical elements.
General information
Logical elements, together with storage elements, form the basis of computers, digital measuring instruments and automation devices. Logic elements perform the simplest logical operations on digital information. They are created on the basis electronic devices, operating in key mode, which is characterized by two key states: “Enabled” - “Disabled”. Therefore, digital information is usually represented in binary form, when the signals take only two values: “0” (logical zero) and “1” (logical one), corresponding to the two states of the key. These two positions (logical 1 and logical 0) constitute the electronic alphabet, or the basis of binary code.
The input of any digital device receives a set of code words, which it converts into other code words or a word. The output codewords are a certain function for which the input codewords are the argument of this function. They are called logical algebra functions.
Logical functions, like mathematical ones, can be written in the form of a formula or table - a truth table, which lists all possible combinations of arguments and the corresponding values of logical functions. A device designed to perform certain functions of the algebra of logic is called a logical element. Let's look at some of them.
Logic element NOT
logical negation (inversion). The logical negation of a statement A is a statement X that is true when A is false..
Logic element AND
Designed to perform a function logical multiplication (conjunction).Logical multiplication is a connection between two simple statements A and B, as a result of which a complex statement X is true only if both statements are true at the same time.
Logic element AND-NOT
Designed to perform a function negation of logical multiplication (negation of conjunction).The negation of multiplication or the Schaeffer function is a connection between two simple statements A and B, as a result of which a complex statement X is false only if both statements are true at the same time.
Work order
Equipment: universal stand, power supply, P1 board, technological maps I-1 - I-9.
1. Analyze the operation of the LED indicator of the stand to determine the levels of logical signals.
2. Examine the operation of logical devices, sequentially using technological maps. Complete the following tasks for each diagram:
A. fill in the truth tables,
b. using the data obtained, identify the logical elements,
V. name the logical algebra functions they perform,
d. designate the logical elements on the diagram with the corresponding symbols,
d. write down formulas expressing the relationship between input and output characteristics.
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Questions for testing 1. What is the purpose and scope of logical elements? 2. Define basic logical functions. 3. Using the LED indicator, determine the level of the logic signal at the output of the circuit. 4. Determine the types of logical elements in the circuit from the output data. 5. Based on the markings of integrated circuits located on the board used, give their characteristics. Laboratory work No. 2. General information More complex digital devices are built from logic elements. One of the most common components of digital technology is the trigger. A trigger is a device that has two stable equilibrium states and is capable of jumping from one state to another under the influence of a control signal. Each trigger state corresponds to a certain (high or low) output voltage level, which can be maintained for any length of time. Therefore, triggers are called the simplest digital automata with memory, i.e. their state is determined not only by input signals in this moment time, but also their sequence in the previous cycles of the trigger. Currently, most flip-flops are based on logic elements in the form of integrated circuits (ICs). They are used as switching elements independently or as part of more complex digital devices, such as counters, frequency dividers, registers, etc. Based on the method of recording information, triggers are divided into synchronous and asynchronous devices. In asynchronous triggers, information is recorded directly with the arrival of input signals. In synchronous (clock) flip-flops, information will be recorded only if there is a clock sync pulse. According to their functional characteristics, triggers are distinguished: with separate triggering (RS-triggers), with delay elements (D-triggers), with counting triggering (T-triggers), universal (JK-triggers). Typically, a trigger has two outputs: forward () and inverse (). The state of the trigger is determined by the voltage at the direct output. Trigger inputs have the following designations: S – separate input for setting the trigger to a single state; R – separate input for setting the trigger to the zero state; D – information input; C – synchronization input; T – counting input and others. The basis of all flip-flop circuits is an asynchronous RS flip-flop. There are two types of RS flip-flops: those built on logical elements “OR-NOT” and those built on logical elements “AND-NOT”. They differ in the level of active signals and have their own designation (see table). RS flip-flops have operating modes: setting to zero or one state, storage, prohibited mode. A forbidden combination (active signals are supplied to both inputs) is implemented when a contradictory command is given: simultaneously set to one and zero states. In this case, the same voltage levels are realized at the direct and inverse outputs, which by definition should not be the case. Clocked D-flip-flops have input D for supplying information (0 or 1) and a clock input C. Synchronization pulses (C = 1) from a special pulse generator are supplied to input C. D flip-flops are free of prohibited combinations of input signals. A counting T flip-flop has one control input T. The trigger states change whenever the control signal changes. T-flip-flops of one type react to the front of a pulse, i.e. for a difference of 0-1, others - for a cut (difference of 1-0). In any case, the frequency of the output pulses is 2 times lower than the frequency of the input pulses. Therefore, T-triggers are used as frequency dividers by 2 or modulo 2 counters. Triggers of this type are not available as ICs. They can be easily created based on D and JK flip-flops. JK flip-flops are universal, they have information inputs J and K and a synchronizing input C. They are used to create counters, registers and other devices. With certain input switching, JK flip-flops can work as RS flip-flops, D flip-flops and T flip-flops. Due to this versatility, they are available in all IC series. Work order Equipment: universal stand, power supply, P2 board, technological cards II-1 - II-4. 1. Select a trigger in the circuit. 2. Complete the following tasks for each diagram: a) write down the name of the trigger, b) make a table of state changes depending on the input signals, indicate active signals with an arrow ( - high level - logical one, ¯ - low level - logical zero), c) determine the type of input (R or S), indicate these designations in the table and indicate on the diagram (for cards II-1 and II-2), d) indicate the operating modes of the trigger, e) draw up a time diagram of trigger states.
Trigger ______________________________________________________________
Trigger ______________________________________________________________
Trigger ______________________________________________________________
Questions for testing 1. What is a trigger? 2. Explain the purpose of flip-flop inputs. 3. What is active signal level? 4. What is the difference between synchronous and asynchronous triggers? 5. Explain the nature of the “forbidden” state in an RS flip-flop. 6. Using the diagram, tell us about the state of the trigger at each cycle of operation. 7. Based on the markings of integrated circuits located on the board used, give their characteristics. Laboratory work No. 3. General information A register is an operational unit consisting of flip-flops and designed to receive and store information in binary code. The length of the codewords written to the register depends on the number of trigger cells that make it up. Because a trigger can only assume one stable state at a given time, then, for example, to write a 4-bit word, you must have a register of four trigger cells. Based on the method of writing code words, parallel, sequential (shifting) and universal registers are distinguished. In parallel registers, the codeword is written in parallel form, i.e. to all trigger cells simultaneously. In a serial register, the codeword is written sequentially, starting from the least significant or most significant digit. All flip-flops included in the register are united by a common synchronization input; some types of circuits have a common input R for the zeroing operation.
Work order Equipment: universal stand, power supply, boards P2, P3, jumper, technological cards II-5, II-6, III-1, III-2. 1. Write down the name of the device indicating its bit capacity. 2. Analyze the operation of two-bit registers. 3. Complete the following tasks for each diagram: a) write down the name of the register, b) write several different code words into the register, enter the results into a table of dependences of output states on input signals, c) draw a symbol for the device, II-5 (P2) |
II-6 (P2)
_______________________________________________________________
Conclusion: ________________________________________________________
________________________________________________________
4. For four-bit registers, complete the tasks:
a) write down the name of the register indicating its capacity,
b) sketch the internal logical structure,
c) write several different code words into the register, enter the results into a table of dependences of output states on input signals,
d) draw a conclusion: how many clock cycles does it take to write one code word in this register?
III-1 (P3)
_______________________________________________________________
| Entrance | Exits | |||
| D | Q4 | Q3 | Q2 | Q1 |
 |
| Entrance | Exits | |||
| D | Q4 | Q3 | Q2 | Q1 |
Conclusion: _________________________________________________________
_________________________________________________________
III-2 (P3)
_______________________________________________________________
| Inputs | Exits | ||||||
| D4 | D3 | D2 | D1 | Q4 | Q3 | Q2 | Q1 |
Conclusion: ___________________________
___________________________
Questions for testing
1. What device is called a register? What is it for?
2. What types of registers do you know? How are they different?
3. Explain the concept of “bit depth”. What does the expression "4-bit register" mean?
4. How do you need to change the functional diagram to get a four-bit register from a two-bit register?
5. How many different words can be written using a 2 (4) bit register?
6. Explain on each functional diagram how you recorded the code word?
Laboratory work No. 4.
General information
Combinational code converters are designed to convert an m-element parallel code at the inputs of a digital machine into an n-element code at its outputs, i.e. to convert a codeword from one form to another. The relationship between input and output data can be specified using logical functions or truth tables. The most common types of code converters are encryptors, decryptors, multiplexers, and demultiplexers.
Encoders are used in information input systems to convert a single signal at one of its inputs into a multi-bit binary code at the outputs. Thus, the signal from each key on the keyboard, indicating a number or letter, is sent to the corresponding input of the encoder, and at its output this symbol is displayed in a binary code word. Decoders perform the reverse operation and are used in information output systems. To visually evaluate the output information, decoders are used together with display systems. One type of indicator is the 7-segment LED or liquid crystal indicator. To do this, the output signals of the decoder are converted into the code of a 7-segment indicator.
Multiplexers solve the problem of selecting information from several sources, demultiplexers solve the problem of distributing information among several receivers. These devices are used in digital technology processor systems to connect individual processor units with each other.
Work order
Equipment: universal stand, power supply, P4 board, technological cards IV-1, IV-2, IV-3.
1. Analyze the operation of the decoder.
2. Complete the following tasks for schemes IV-1 and IV-2:
a) make a table of the dependence of output states on input signals,
b) draw a conclusion: from which coding system does the device translate to which?
c) how many digits does a binary number have in circuit IV-2? What task does the SA5 toggle switch perform?
Multiplexer
3. Analyze the operation of a circuit containing a multiplexer and complete the tasks:
a) find the multiplexer in the diagram,
b) check where the information comes from at the multiplexer inputs,
c) check what device is used to set the address to the multiplexer,
d) set the multiplexer the address of the information input from which you want to send the signal to its output,
e) fill out the table of the dependence of the output signal on the input information and the address given to the multiplexer, entering different addresses and supplying different information to the inputs.
| Address | No. D-input connected to the output | Input information | Output Y | |||||||||
| A2 | A1 | A0 | D0 | D1 | D2 | D3 | D4 | D5 | D6 | D7 | ||
Questions for testing
1. What device is called a decoder? What is it for?
2. What device is called a multiplexer? What is it for?
3. What type of indication is used in scheme IV-2?
4. What does the expression “binary information coding system” (decimal, hexadecimal) mean?
To describe the algorithm of operation of logic circuits, the mathematical apparatus of logic algebra is used. The algebra of logic operates with two concepts: an event is true (logical "1") or an event is false (logical "0"). Events in the algebra of logic can be connected by two operations: addition (disjunction), denoted by the sign U or +, and multiplication (conjunction), denoted by the sign & or dot. An equivalence relation is indicated by an = sign, and a negation is indicated by a bar or an apostrophe (") above the corresponding symbol.
Logic circuit has n inputs, which correspond to n input variables X 1 , ... X n and one or more outputs, which correspond to output variables Y 1 .... Ym. Input and output variables can take two values: X i = 1 or X i = 0.
The switching function (SF) of a logic circuit connects input variables and one of the output variables using logical operations. The number of PFs is equal to the number of output variables, and the PF can take values 0 or 1.
Logical operations. The following elementary operations (functions) are of greatest practical interest.
Logical multiplication (conjunction),
Logical addition (disjunction),
Logical multiplication with inversion,
Logical addition with inversion,
Summation modulo 2,
Equivalence.
Logic elements. There are digital integrated circuits, corresponding to basic logical operations. Logical multiplication corresponds to the logical element "AND". Logical addition corresponds to the logical element "OR". Logical multiplication with inversion - logical element "AND-NOT". Logical addition with inversion - logical element "OR-NOT". The inversion operation corresponds to the logical element "NOT". There are microcircuits that implement many other logical operations.
Truth tables. The main way to specify the PF is to compile a truth table, in which the PF value (0 or 1) is indicated for each set of input variables. The truth table for the logical element "NOT" (logical operation) has the form
| Input X | Output Y |
1.1. Study of the characteristics of the logical element "OR-NOT"
The diagram for studying the logical element "OR-NOT" is shown in Fig. 1.
In the diagram fig. 1 logic gate inputs "OR NO" connected to a word generator that forms a sequence of binary numbers 00, 01, 10 and 11. The right (low-order) binary digit of each number corresponds to the logical variable X1, the left (most significant) to the logical variable X2. The logic element inputs are also connected logic probes, which light up red when a logical “1” is received at this input. The output of the logic element is connected to a logic probe, which lights up red when a logic “1” appears at the output.
Construction of a circuit for studying the logical element "OR-NOT"
Launch using the desktop shortcut Windows desktop program Electronics Workbench.
Construction of the diagram in Fig. 1 will be carried out in two stages: first we will place it as shown in Fig. 1 pictograms of elements, and then connect them in series.
1. Click the button
component and instrumentation library panels. From the logical element window that appears, pull out the logical element icon NOR("OR NO").
2. Click the button
From the window that appears, sequentially pull out the logic probe icons.
3. Unfold the logic probes as shown in Figure. 1. To do this, use the rotate button on the function panel
4. Click the button
component and instrumentation library panels. From the indicator window that appears, pull out the icon word generator
5. Place the element icons using the towing method as shown in Fig. 1 and connect the elements according to the figure.
6. Double-click to open the front panel word generator.
On the left side of the panel word generator The code combinations are displayed in hexadecimal code, and in the lower part - in binary code.
7. Fill the hexadecimal code window with code combinations, starting with 0 in the top zero cell and then adding 1 in each subsequent cell. To do this, click on the button and in the preset window that appears, enable the option Up counter and click on the button Accept.
8. In the window Frequency set the frequency of generating code combinations to 1 Hz.
The sequences of binary numbers 00, 01, 10 and 11 correspond in hexadecimal code - 0, 1, 2, 3. Let's program the generator to periodically generate the specified sequence of numbers.
9. Type in the window Final number 0003 click on the button Cycle.
10. Start the simulation process using the switch. Observe at what combinations of input signals a “1” appears at the output of the logic element. Clicking the button Step, fill in the truth table for the "OR-NOT" element in the Report. Stop the simulation process using the switch.
11. Save the file in a folder with your Last name under the name Zan_17_01 .
