Research of logical elements and synthesis of logical circuits. Set for the study of the operation of logic elements Study of logic elements
To describe the operation algorithm of logic circuits, the mathematical apparatus of logic algebra is used. The algebra of logic operates with two concepts: the event is true (logical "1") or the 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 denoted by =, and negation by a bar or an apostrophe (") above the corresponding symbol.
Logic diagram has n inputs that correspond to n input variables X 1 , … X n and one or more outputs that correspond to output variables Y 1 …. Y m . Input and output variables can take two values X i = 1 or X i = 0.
The switching function (SF) of the logic circuit connects the input variables and one of the output variables using logical operations. The number of PF is equal to the number of output variables, while the PF can take the values 0 or 1.
Boolean operations. The following elementary operations (functions) are of the greatest practical interest.
Boolean multiplication (conjunction),
Logical addition (disjunction),
Boolean multiplication with inversion,
Logical addition with inversion,
Modulo 2 summation,
Equivalence.
Logic elements. There are digital integrated circuits corresponding to the 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 set the PF is to compile a truth table, in which the value of the PF (0 or 1) is indicated for each set of input variables. The truth table for the logical element "NOT" (logical operation) is
| Input X | Output Y |
1.1. Study of the characteristics of the logical element "OR-NOT"
The scheme for studying the logical element "OR-NOT" is shown in fig. one.
On the diagram of Fig. 1 gate inputs "OR NO" connected to a word generator that generates a sequence of binary numbers 00, 01, 10 and 11. The right (lowest) binary digit of each number corresponds to the logical variable X1, the left (highest) - to the logical variable X2. The inputs of the logic element 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.
Building a research circuit for the logical element "OR-NOT"
Launch via desktop shortcut Windows program Electronics Workbench.
Construction of the circuit fig. 1 will be done 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 libraries and instrumentation panels. From the window that appears logical elements pull out the gate icon NOR("OR NO").
2. Click the button
From the window that appears, pull out the logical probe icons in sequence.
3. Expand the logic probes as shown in fig. 1. To do this, on the function bar, use the rotate button
4. Click the button
component libraries and instrumentation panels. From the indicator window that appears, pull out the icon word generator
5. Arrange the icons of the elements 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 code combinations are displayed in hexadecimal code, and at the bottom - in binary.
7. Fill in the hexadecimal code window with code combinations, starting with 0 in the upper zero cell and then adding 1 in each subsequent cell. To do this, click on the button, in the window that appears, turn on the option Up counter and click on the button accept.
8. In the window Frequency set the pattern generation frequency to 1 Hz.
The sequence of binary numbers 00, 01, 10 and 11 corresponds in hexadecimal code - 0, 1, 2, 3. Let's program the generator to generate the specified sequence of numbers periodically.
9. Dial in the window Final number 0003 click on the button cycle.
10. Start the simulation process using the switch. Watch for which combinations of input signals a "1" will appear at the output of the logic element. Clicking the button step, fill in the truth table for the element "OR-NOT" in the Report. Stop the simulation process with the switch.
11. Save the file in the folder with your Surname under the name Zan_17_01 .
1. The purpose of the work
The aim of the work is:
Theoretical study of logical elements that implement the elementary functions of the algebra of logic (FAL);
Experimental study of logical elements built on domestic microcircuits of the K155 series.
2. Basic theoretical provisions.
2.1. The mathematical basis of digital electronics and computer technology is the algebra of logic or Boolean algebra (named after the English mathematician John Bull).
In Boolean algebra, independent variables or arguments (X) take only two values: 0 or 1. Dependent variables or functions (Y) can also take only one of two values: 0 or 1. The Boolean Algebra Function (FAL) is represented as:
Y \u003d F (X 1; X 2; X 3 ... X N).
This form of setting the FAL is called algebraic.
2.2. The main logical functions are:
Logical negation (inversion)
;Logical addition (disjunction)
Y = X 1 + X 2 or Y = X 1 V X 2 ;
Logical multiplication (conjunction)
Y \u003d X 1 X 2 or Y \u003d X 1 L X 2.
More complex logic algebra functions include:
Equivalence (equivalence) function
Y = X 1 X 2 +
or Y = X 1 ~ X 2 ;Disparity function (modulo two addition)
+ X 2 or Y \u003d X 1 X 2;Pierce function (logical addition with negation)
;Schaeffer function (logical multiplication with negation)
;2.3. The following laws and rules are valid for Boolean algebra:
distributive law
X 1 (X 2 + X 3) \u003d X 1 X 2 + X 1 X 3,
X 1 + X 2 X 3 = (X 1 + X 2) (X 1 + X 3) ;
Recurrence rule
X X = X , X + X = X ;
Negation rule
= 0 , X + = 1 ;De Morgan's theorem
= , = ;Identities
X 1 = X , X + 0 = X , X 0 = 0 , X + 1 = 1.
2.4. Circuits that implement logic functions are called logic elements. The main logical elements have, as a rule, one output (Y) and several inputs, the number of which is equal to the number of arguments (X 1; X 2; X 3 ... X N). In electrical diagrams, logical elements are indicated as rectangles with pins for input (left) and output (right) variables. Inside the rectangle is a symbol indicating the functional purpose of the element.
Figure 1 ¸ 10 shows the logical elements that implement those discussed in paragraph 2.2. functions. The so-called state tables or truth tables are also presented there, describing the corresponding logical functions in binary code in the form of states of input and output variables. The truth table is also a tabular way of specifying the FAL.
Figure 1 shows the element “NOT”, which implements the function of logical negation Y =
.
The “OR” element (Fig. 2) and the “AND” element (Fig. 3) implement the functions of logical addition and logical multiplication, respectively.
Pierce's functions and Schaeffer's functions are implemented using the "OR-NOT" and "AND-NOT" elements shown in Fig. 4 and Fig. 5 respectively.
The Pierce element can be represented as serial connection the “OR” element and the “NOT” element (Fig. 6), and the Schaeffer element - in the form of a serial connection of the “AND” element and the “NOT” element (Fig. 7).
Fig.8 and Fig.9 show the elements “XOR” and “XOR - NOT”, realizing the functions of inequivalence and inequivalence with negation, respectively.
2.5. Logical elements that implement the operations of conjunction, disjunction, Pierce and Schaeffer functions can be, in general, n - input. So, for example, a logical element with three inputs that implements the Pierce function has the form shown in Fig. 10.
In the truth table (Fig. 10), in contrast to the tables in clause 2.4. there are eight values of the output variable Y. This number is determined by the number of possible combinations of input variables N, which, in general, is equal to: N = 2 n , where n is the number of input variables.
2.6. Logic elements are used to build integrated circuits, performing various logical and arithmetic operations and having different functional purposes. Microcircuits of the K155LN1 and K155LA3 types, for example, have six inverters and four Schaeffer elements, respectively (Fig. 11), and the K155LR1 microcircuit contains elements of various types (Fig. 12).
2.7. FAL of any complexity can be implemented using the specified logical elements. As an example, consider the FAL, given in algebraic form, in the form:
. (1)Simplify this FAL using the above rules. We get:
(2)
The operation carried out is called FAL minimization and serves to facilitate the procedure for constructing a functional diagram of the corresponding digital device.
The functional diagram of the device that implements the considered FAL is shown in Fig.13.
It should be noted that the function (2) obtained after transformations is not completely minimized. Full minimization of the function is carried out in the course of the laboratory work.
3. Description of the object and means of research
The device studied in the laboratory work is shown in Fig.14.
3.1. The device is a group of logical elements made on K155 series microcircuits (elements DD1¸DD4).
For microcircuits of this series, the voltage U 1 \u003d (2.4 ¸ 5.0) V corresponds to a logical unit, and U 0 \u003d (0 ¸ 0.8) V corresponds to a logical zero.
3.2. Logical “0” and “1” at the input of the elements are set using the buttons located on the front panel of the K32 block under the inscription “Code programmer”. The numbers of the buttons on the panel correspond to the numbers on the device diagram.
Complete graphic image buttons of this type(so-called “latching buttons”) is shown only for the SA1 button.
When the button is pressed, the input of the elements through the resistor R1 is connected to a source with a voltage of 5V. In this case, the voltage U 1 will act at the input of the elements, which corresponds to the supply of a logical unit to the output of the microcircuit. When the button is released, the input of the element will be connected to the bus, which is under the ground potential, which corresponds to applying a logical zero U 0 to the output of the microcircuit.
3.3. Logic signals from the outputs of the elements DD1 ¸ DD4 arrive at digital indicators and are induced in the form of symbols “0” and “1”. The digital indicators are located in block K32 on the left (“IO \ 2” button) under the indicators must be pressed.
3.4. The signal from the output of the DD5 element is fed through the switching circuits to the input of the H3014 multimeter. The multimeter is preliminarily set to the “-V” DC voltage measurement mode and the following connections are made:
3.4.1. The input - multimeter socket “-V” - is connected with a cable to the socket “Output V ~“ of block K32.
3.4.2. Socket XS1 on the board of the device is connected by a conductor to the left socket under the inscription “Input 1” in the field of the inscription “Switch”.
3.4.3. The button “SV \ VNK” above the above socket must be in the pressed state.
3.4.4. The button “VKh 1” under the inscription “Control V ~“ must be in the pressed state, and the button “SV \ VNK” in the field of the inscription “KVU” must be in the depressed state.
4.1. Research of features of functioning of logical elements DD1 ¸ DD4 and definition of their functional purpose.
Objective . Acquaintance with the basic functions and laws of the algebra of logic, the characteristics of logic circuits, the basics of analysis and synthesis of simple and complex logic circuits.
Brief theoretical information.
Job analysis digital devices and the synthesis of logical circuits is based on the mathematical apparatus of the algebra of logic or "Boolean" algebra, which operates with only two concepts: true (logical "1") and false (logical "0"). Functions that display such information, as well as devices that form functions of the algebra of logic, are called logical. Logical functions of several variables determine the nature of logical operations, as a result of which a set of input variables x 0 , x 1 ,…, x n -1 the output variable is assigned F
F = f(x 0 , x 1 ,…, x n -1 ).
The transformation function is characterized by a table in which each combination of input variables corresponds to the value of the output variable F. It is called the truth table.
The main functions of the algebra of logic, with the help of which any logical transformations can be carried out, are logical multiplication (conjunction), logical addition (disjunction) and logical negation (inversion).
The algebra of logic allows you to transform formulas that describe complex logical dependencies in order to simplify them. This ultimately helps to determine the optimal structure of a digital automaton that implements any complex function. Under the optimal structure, it is customary to understand such a construction of an automaton, in which the number of elements included in its composition is minimal.
Basic laws of the algebra of logic.
displacement law:
a + b = b+ a;ab = ba.
Combination law:
(a + b) + c = a + (b + c); (ab)c = a(bc).
Distributive law:
a(b + c) = ab + ac; a + bc = (a + b)(a + c).
Absorption law:
a + ab = a(1 + b) = a; a(a + b) = a + ab = a.
Bonding law:
ab
+
a
=
a;
(a
+
b)(a
+
)
=
a.
The law of negation:
or
.
Logic elements. Logic elements use only two levels as input and output voltage values: “high” and “low”. If logical "0" corresponds to a low-level voltage, and logical "1" to a high one, then such logic is called positive, and vice versa, if a high-level voltage is taken as a logical "0", and a low-level voltage is taken as a logical "1", then such logic is called negative. In transistor-transistor logic (TTL), the logic "0" voltage is - U 0 is tenths of a volt (less than 0.4 V), and the voltage of the logical "1" - U 1 >2.4 V. Logic elements implement the simplest functions or a system of functions of the algebra of logic.
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Table 1 |
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The simplest function of the algebra of logic is the NOT function. It is implemented using an inverter, the conventional graphic designation of which is shown in fig. 1. The input of the inverter is the value X, which can take two values: "0" and "1". output value Y, while also taking two values: "1" and "0". One-to-one correspondence X and Y is given by the truth table (Table 1), and the value of the output value Y does not depend on previous values, but only on the current value of the input variable X:
Y
=
.This is true for all logical elements that do not have memory, which in the truth table have the value Y does not depend on the order of the lines.
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Table 2 |
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The logical elements that implement the functions of logical addition and logical multiplication are the OR and AND elements. Truth tables for these elements uniquely link the value of the output quantity Y with the values of two (or more) input quantities X l ,
X 2
,
... x n. Conditional graphic symbols logic elements OR and AND are shown respectively in fig. 2 and 3, and their truth tables are in tables 2 and 3. For example, for a 2-OR logic element that implements a disjunction Y= x l + X 2 or Y= x l X 2 ,
and for the 2-I element, which implements the conjunction
Y= x l X 2 or Y= x l X 2 .
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Table 3 |
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on a set of logical elements AND, OR, NOT, you can implement any arbitrarily complex logical function, therefore this set elements is called functionally complete. In practice, an extended set of logical elements is often used, which also makes it possible to compose functionally complete systems. These include elements:
OR-NOT (Pierce element) that implements the function
;
AND-NOT (Scheffer element) that implements the function
.
Their designations and truth tables are shown in fig. 4 and in table. four.
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Table 4 |
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In particular, functionally complete systems can consist of elements of only one type, for example, those that implement the NAND or NOR function.
Combinational logic circuits are such circuits, the output signals of which are uniquely determined by the signals present at their inputs at the considered moment of time and do not depend on the previous state.
The set of logical elements included in the training stand on the basics of digital technology does not contain elements that implement the OR-NOT function, which limits the number of options for constructing logical circuits during their synthesis and allows you to draw up circuits only in the basis of NAND elements.
Before proceeding to the analysis and synthesis of logical devices in a given basis of elements (AND-NOT), it is necessary to compile a table in which all possible forms of representing the output signals of these elements will be summarized, provided that logical variables are applied to their inputs X l and X 2 . When synthesizing circuits, two techniques can be used: double inversion of the input source expression or its part and the application of De-Morgan's theorems. In this case, the function is converted to a form containing only the operations of logical multiplication and inversion, and is rewritten using conventions operations AND-NOT and NOT.
The sequence of analysis and synthesis of combinational logic circuits:
Drawing up a table of functioning of a logical circuit (truth table).
Logic function entry.
Minimization of a logical function and its transformation to a form convenient for implementation in a given basis of logical elements (AND-NOT, NOT).
An example of the analysis and synthesis of logical circuits .
Let it be necessary to construct a majority cell (voting cell) for three inputs, i.e. a cell whose output signal is equal to one when two or three inputs of the circuit have a one signal, otherwise the output signal must be equal to zero.
First, fill in the truth table (Table 5). Since in this case there are three input signals X 1 , X 2 , X 3 , each of which can take one of two possible values (0 or 1), then there can be eight different combinations of these signals in total. Four of these combinations will correspond to the output signal F, equal to one.
Table 5
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x 1 |
x 2 |
x 3 | ||
If in the synthesized truth table the output value often takes the value "1", then rows are synthesized in which the output value is "0".
When performing the given procedure, we obtain the function
F= . (1)
To minimize (simplify) this function, you need to apply the basic laws of the algebra of logic. The following sequence of transformations is possible, for example, using the gluing law (De Morgan's theorem):
F = =
+
=
. (2)
As you can see, the resulting final expression is much simpler than the original one.
Similarly, analysis is carried out (compilation of truth tables) and more complex logical circuits.
To complete the task, a set of the most common logical elements is proposed (Fig. 5).
Rice. 5. A set of logical elements to complete the task
Assignment for laboratory work
1. Compile truth tables for all logical elements shown in fig. 5.
2. For each logical element from the set presented in fig. 5. compose logical expressions that implement their functions in the basis of logical elements NOT and AND-NOT and draw the resulting identical circuits.
3. Collect the considered schemes on the stand and, by sorting out combinations of input signals, compile their truth tables.
4. Using the laws of negation (De-Morgan's theorems), transform the minimized function (2) to implement it in the basis of logical elements NOT and NAND and draw the resulting identical circuit.
5. Assemble the presented circuit on the stand and, by sorting out combinations of input signals, check the compliance of its operation with the truth table (Table 5).
Test questions
What is functional complete system and the basis of logical elements?
What are the features of the synthesis of logical devices?
What are the principles of minimizing logical devices?
Name the basic operations of Boolean algebra.
What are the theorems of Boolean algebra? Formulate De Morgan's theorems: absorption and gluing.
What digital devices are called combinational?
LAB #5
This set allows you to study the logic of the main types of logic elements. The set is housed in a black plastic box sized 200 x 170 x 100 mm.
The installation contains four modules of standard size 155 x 95 x 30 mm. In addition, there should be connecting wires, but in the copy that the author dealt with, they were absent, but the instruction manual was preserved.
Logic element AND
The first module is a logic element And, a signal appears at its output only if the signal comes to both of its information inputs.
The standard module is printed circuit board, which is closed on top with a transparent plastic cover, fixed with two screws.
The module is easily disassembled, which allows you to examine the circuit board of the device in detail. On the back side, the printed conductors are covered with an opaque plastic cover.
OR gate
The logical element is almost similarly arranged OR, a signal appears at its output provided that a signal arrives at any of its information inputs.
Gate NOT
Logic element NOT. The input and output signals 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.
In general, this digital electronics kit is similar to the Electronic Amplifier kit. Of course, the implementation of logical elements presented in the set is far from being the only one. In fact, logical elements are implemented here, as it was done in the 60s of the XX century. In this case, it is important that when working with this set, you can directly study the simplest circuit example underlying the very basis of digital semiconductor electronics. Thus, a separate logical element ceases to be a "black box" that operates on pure magic. Highly visible and protected at the same time circuit diagram, this is just what you need to learn the basics of electronics. The author of the review is Denev.
transcript
1 16 The study of the logic of the operation of logical elements The purpose of the work The purpose of the work is to consolidate knowledge of the basics of the algebra of logic and gain skills in the study of logical elements and connecting them into the simplest combinational circuits.
2 17 to 1. Information from the theory combinational circuits consist of logical elements. A logical element is the simplest part of a digital circuit that performs logical operations on logical variables. When using integrated circuits, such elements are usually elements of the AND-NOT, OR-NOT, AND-OR-NOT type. The work of logical elements is described by truth tables. On electrical functional diagrams, logical elements are displayed in the form of conventional graphic symbols (UGO). Conditional graphic designations of logical elements for two inputs are shown in Fig. 2.1a 2.1d. The truth tables for these elements have the form shown in Table NOT 2I 2OR 2I-NOT 1 1 a) b) c) d) e) element a b NOT 2AND 2OR 2AND-NOT 2OR-NOT Y = a Y = ab Y = a v b Y = ab Y = a v b line 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. Further, if necessary, the resulting function should be minimized.
3 18 2. Short description laboratory setup As a laboratory setup, a stand of the UM-11 type is used. The stand is based on a power supply, clock and single pulse generators, a set of logic elements and triggers, as well as display 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 conditional graphic designations of logical elements and triggers. With the help of special wires with tips, you can connect elements to each other, apply signals from generators or switches to the inputs of the elements, and also observe the signal values using indicator lights or using an oscilloscope. A fragment of the front panel of the stand is shown in Fig. Fig. 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, there is also an NAND element for 8 inputs on the front panel. Such a 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 work.
4 19 3. Work order Task 1. Explore the logic of the 2I-NOT element. To do this, assemble on the stand the circuit shown in Fig. When constructing the circuit, use switches, with the help of which signals “0” and “1” can be applied to the input of the element. output signals to observe the status 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 top output of the switch you can get the direct value of the variable, and from the bottom 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 reversed. Using the switches, apply all combinations of signals "a" and "b" to the input of the circuit and enter the obtained values of the output signals into the truth table. Compare the resulting table with the data in Table. 2.1.for the element 2I-NOT. Enter in the report: the assembled circuit, the UGO of the 2I-NOT element and the resulting truth table. +5V a1 a b Y 1 b To do this, assemble a circuit similar to the circuit in Fig. Check the logic of the circuit for various values of input signals and compile a truth table. Task 3. Explore the logic 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 the NOT circuit on 2I-NOT elements
5 20 Check the logic of the circuit for 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. Make a truth table and compare it with the data in Table. 2.1 for element 2I. Fig Scheme of the implementation of the circuit AND on the elements of AND-NOT Task 5. Assemble the circuit shown in Fig. 2.6 and examine the logic of its operation. Make a truth table and compare it with the data in Table. 2.1 for element 2OR. Fig Scheme of the implementation of the OR circuit on the elements of AND-NOT Task 6. Assemble the circuit shown in fig. 2.7 and explore the logic of its operation. Make a truth table and compare it with the truth table for the element 2AND-2OR. Fig An example of a scheme on the elements of AND-NOT 4. Content of the report 1. Theme, the purpose of the work, 2. The results of the tasks. For each task, bring the scheme of the experiment, the UGO of the element under study and the truth table. 3. Analysis of the obtained results. 4. Conclusions on the work.
6 21 5. Test questions 1. What is a logical function? 2. What is a logic element? 3. Explain the logic of the NOT element. 4. Explain the logic of the AND element. 5. Explain the logic of the OR element. 6. Explain the logic of the AND-NOT element. 7. Explain the logic of the OR-NOT element. 8. What is a truth table? 9. How to write a logical function in SDNF according to the truth table? 10. How to build a NOT circuit from AND-NOT elements? 11. How to build an AND circuit from AND-NOT elements? 12. How to build an OR circuit from AND-NOT elements? 13. What function does the circuit shown in fig. 2.7.
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FEDERAL RAILWAY TRANSPORT AGENCY Federal State Budgetary Educational Institution of Higher Professional Education "MOSCOW STATE UNIVERSITY OF TRANSPORT"
MINISTRY OF EDUCATION AND SCIENCE of the Russian Federation R.E.
LABORATORY WORK 1 SYNTHESIS OF COMBINATION DEVICES ACCORDING TO A GIVEN LOGIC FUNCTION Purpose of the work: 1. Study of methods for synthesizing combinational devices according to a given logical function. 2. Construction of combinational
Laboratory work 9 Simulation of combinational devices The purpose of the work is to study the forms of representation of numbers in digital devices and to study the circuits of combinational digital devices of decoders, multiplexers
FEDERAL AGENCY FOR EDUCATION STATE EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION "VORONEZH STATE UNIVERSITY" LOGICAL ELEMENTS Guidelines
Logical models of switching circuits Information processing Physical principle of information processing The information to be converted is encoded by a sequence of pulses, the processing of which takes place
Job. Synchronous single-stage triggers with static and dynamic recording control
Laboratory work 11 Simulation of pulse counters The purpose of the work is to study the structure and study the operation of adding and subtracting binary counters, as well as counters with a conversion factor that is different
Laboratory work 2. Triggers Purpose: To study the purpose and principle of operation of trigger devices. Introduction to basic trigger devices from the EWB library. Equipment: Electronic Lab Electronics
ELEMENTS OF AUTOMATIC SYSTEMS Topic 2 Logic circuits and their minimization I.V. Muzylev 23 Basic concepts of the algebra of logic http://cifra.studentmiv.ru Logic circuits Compilation of truth tables for logical
4. LABORATORY WORK 3 RS AND D-TRIGGER The purpose of the lesson: building and familiarizing with the operation of the main circuits of RS and D flip-flops using the tools of the digital part of the EWB package, consolidating the theoretical
1. PURPOSE OF THE WORK 1.1. To study the functional and electrical characteristics of the ALU on the IC K155 IP3. 1.2. Obtain practical skills in researching the operation of ALU ICs by applying inputs, observing
1. PURPOSE OF THE WORK 1.1. To study the functional and electrical characteristics of the decoders on the IC K 155 ID4; K 155 ID7; 1.2. Get practical skills in researching the operation of decoder ICs by submitting
Topic 4. Logical foundations of computers 1. BASIC INFORMATION FROM THE ALGEBRA OF LOGIC ... 1 2. LAWS OF THE ALGEBRA OF LOGIC ... 4 3. THE CONCEPT OF MINIMIZATION OF LOGICAL FUNCTIONS ... 6 4. TECHNICAL INTERPRETATION OF LOGICAL FUNCTIONS ...
Direction 09.03.03 Informatics 1.2 Lecture "Logical foundations of informatics" Lecturer Molnina Elena Vladimirovna Senior lecturer of the department Information systems, room 9, main building. mail: [email protected]
LABORATORY WORK STUDY OF ELECTRIC PROCESSES IN SIMPLE LINEAR CIRCUITS The purpose of the work: to study the transfer coefficient and phase shift between current and voltage in circuits consisting of series
Control task Depending on the issued version, you need to build a CLS of a decoder, encoder, multiplexer or adder. Option 7 to decimal: "7" 7 "7" 7 0 0 0 0 0 0 0 5 0 0 0 0 0
Amendment and you have every chance to learn to understand people. As a result of the study, it was revealed that most of the students use sign language and partially understand the meaning of body movements.
3 Lecture 3. COMBINATION DIGITAL DEVICES Plan. Encoders, decoders and code converters. Multiplexers and demultiplexers. 3. Adders.. Conclusions.. Encoders, decoders and converters
Electronics and MPT Synthesis of logical circuits according to a given function Representation of logical functions (LF) 3 ways of representing logical functions:. graph (in the form of a voltage time diagram); 2. analytical
STUDY OF ELEMENTARY LOGIC ELEMENTS Guidelines Ulyanovsk 2006 1 Federal Agency for Education State educational institution of higher professional education
Ministry of Education and Science of the Russian Federation Federal State Autonomous Educational Institution of Higher Professional Education Kazan (Volga Region) Federal University
LABORATORY WORK "FUNDAMENTALS OF DIGITAL TECHNOLOGY" Fig. 1. General view of the laboratory stand 1 Work 1 STUDY OF RECTANGULAR PULSES GENERATORS 1. Purpose of work Familiarization with the main functions and testing
MINISTRY OF STUDIES AND SCIENCES OF UKRAINE NATIONAL METALLURGICAL ACADEMY OF UKRAINE METHODOLOGICAL EXPOSURE TO VISOKANNYA LABORITORY ROBIT AND PARTICULAR WORK IN THE DISCIPLINE "COMP UTTERIV ARCHITECTURE" FOR STUDENTS
MINISTRY OF TRANSPORT OF THE RUSSIAN FEDERATION STATE CIVIL AVIATION SERVICE MOSCOW STATE TECHNICAL UNIVERSITY OF CIVIL AVIATION Department of Computers, Complexes, Systems and Networks Coursework
(basic concepts - compilation of complex expressions - truth tables - laws of propositional logic - examples) The initial concept of propositional logic is a simple or elementary proposition. it
Laboratory work 3 Schemes on D-flip-flops Department of the Sun SibGUTI 2012 Contents 1. Objectives of the work: ... 3 2. Trigger in counting mode ... 3 3. Divider ... 3 4. Description of microcircuits K176TM1 and K176TM2 ... 4 5.
ARCHITECTURE OF COMPUTERS AND COMPUTING SYSTEMS Lecture 3. Logical foundations of computers, elements and nodes. Lecturer Tsveloy Vladimir Andreevich PURPOSE: TO STUDY THE BASIC OPERATIONS OF THE ALGEBRA OF LOGIC, THE BASIS OF CONSTRUCTING COMBINATIONAL
Chapter 3 LOGIC AND LOGICAL FOUNDATIONS OF THE COMPUTER 3.1. Algebra of logic The first teachings about the forms and methods of reasoning arose in the countries of the Ancient East (China, India), but modern logic is based on
1 The simplest information converters Mathematical logic with the development of computers turned out to be in close relationship with computational mathematics, with all issues of design and programming
1. PURPOSE OF THE WORK 1.1. To study the functional and electrical characteristics of semiconductor ROMs on ICs K155PR6, K155PR7. 1.2. Get practical skills in researching the operation of IC ROM K155PR6, K155PR7
Contents Preface 14 Chapter 1. Digital systems and presentation of information 19 1.1. Digital systems 19 1.1.1. Control systems 20 Logic signals and functions 21 Positive and negative logic
Ministry of Education and Science of the Russian Federation Federal State Budgetary Educational Institution of Higher Professional Education Nizhny Novgorod State Technical University. R.E.
A.I. Nedashkovsky Laboratory work Asynchronous and synchronous pulse counters The purpose of the work is knowledge of the construction structures, parameters and modes of operation of pulse counters, the ability to analyze their work,
Ministry of Education of the Russian Federation ORENBURG STATE UNIVERSITY Department of Instrument Engineering E. A. Kornev METHODOLOGICAL INSTRUCTIONS for laboratory work in the disciplines " Computer Engineering»,
Open lesson “Construction of logic circuits. Basic logical elements". Type of lesson: combined (testing students' knowledge, learning new material). Class: 10 A class Date: 17.01.2009
Laboratory work 2. Research of work of triggers. Department of the Armed Forces SibGUTI 2012 Contents 1. The purpose of the work: ... 3 2. General information ... 3 3. Asynchronous RS-trigger ... 4 4. Synchronous single-stage D-trigger ....
PROCEDURE OF PERFORMING WORK Task for work To measure vibrations at installation of the car without shock-absorbers and with shock-absorbers. Based on the measurement results, determine the effectiveness of the vibration isolation of the machine. In complicated
