Logic Gate Diagrams

8 Key excerpts on "Logic Gate Diagrams"

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  eBook - ePub

  Electronics

  from Classical to Quantum

  • Michael Olorunfunmi Kolawole(Author)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  2 Functional Logics

  Many tasks in modern computer, communications, and control systems are performed by logic circuits. Logic circuits are made of gates . A logic gate is a physical device that implements a Boolean function that performs a logic operation on one or more logical inputs (or terminals) and produces a single logical output. This chapter examines the basic principles of logic gates: the types—from primitive to composite gates—and how they are arranged to perform basic and complex functions.

  2.1 The Logic of a Switch

  Basic logic circuits with one or more inputs and one output are known as gates . Logic gates (or simply gates ) are used as the building blocks in the design of more complex digital logic circuits. A logic gate is a physical device that implements a Boolean function that performs a logic operation on one or more logical inputs (or terminals) and produces a single logical output. Practically, gates function by “opening” or “closing” to allow or reject the flow of digital information. For any given moment, every terminal is in one of the two binary conditions “0” (low) or “1” (high). These binary conditions represent different voltage levels; that is, any voltage v up to the device threshold voltage, V th , (i.e. 0 ≤ v ≤ V th ); and in the conduction ranges 0 ≤ v ≤ 2.5 V and 2.5 < v ≤ 5 V represent logic states “0” and “1,” respectively.

  Note that machine arithmetic is accomplished in a two-value (binary) number system, but Boolean algebra—a two-value symbolic logic system—is not a generalization of the binary number system. The symbols 0, 1, +, and • are used in both systems but with totally different meanings in each system. (The meanings of these symbols become obvious during discussions in the next paragraphs.) This symbolic tool allows us to design complex logic systems with the certainty that they will carry out their function exactly as intended. Conversely, Boolean algebra can be used to determine exactly what function an existing logic circuit was intended to perform. So, writing Boolean functional expressions allows us to observe the expected output logic of the simple or complex gates’ design or construction.

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  eBook - ePub

  Basic Electricity and Electronics for Control: Fundamentals and Applications, Third Edition

  • Lawrence Thompson(Author)
  • 2006(Publication Date)
  • International Society of Automation

    (Publisher)

  Chapter 17 DIGITAL LOGIC

  Digital logics are the building blocks of the digital revolution. From simple gates to highly complex application-specific integrated circuits (ASICs), digital logic is found everywhere. While this chapter is not a comprehensive review of all current digital logic (that would take several volumes), it will introduce you to various logic families and functions.

  FUNCTIONS

  All digital circuitry consists of combinations of ANDs, ORs, XORs, NEGATEs, NORs, NANDs, counters, registers, and memory. In the beginning, logics were manufactured out of discrete components. This gave way to small-scale integration (SSI) and very quickly into large-scale integration (LSI). Today, a central processing unit (CPU) (microprocessor) is made up of millions of gates, registers, and counters.

  To gain an understanding of digital logic a good place to start is with the gate circuits.

  GATES

  There are but four basic gate structures, just four. Complex logic is built out of various combinations of these gates. They are quite simple to understand. While all the gates discussed here have just two inputs, understand that gates may have many more than two inputs. The logic is the same.

  OR

  The rule for the OR gate is simple. A 1 on any input will give a 1 on the output. Referring to a two-input OR gate, the rule reads, “A 1 on input A OR a 1 on input B will cause the output to be a 1.” Figure 17–1 illustrates the OR symbol, and Figure 17–2 shows a map of the logic.

  To read the logic math, note that the inputs are on the outside, as an example A = 1 and B= 0. If you start at the A=1 row (top) and move down into the block 1 row, that is the B=0 row. The value in that intersecting block is the output, in this case a 1. Note that if either A or B is a 1, the output is a 1.

  Figure 17–1 An OR gate.

  Figure 17–2 Logic map for an OR.

  AND

  The AND gate rules are also simple. All inputs must have a 1 for the output to be a 1. For the two-input AND: “It takes a 1 on input A AND a 1 on input B to have a one on the output.” Figure 17–3 is the symbol for an AND; Figure 17–4

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  eBook - ePub

  Electronics in easy steps

  • Bill Mantovani(Author)
  • 2019(Publication Date)
  • In Easy Steps Limited

    (Publisher)

  13

  Digital Electronics

  Here, you will learn all about digital circuits and logic gates. You are introduced to the basic logic gates that are the building blocks for digital circuits, and will learn how a truth table is used to identify the function of a gate or logic circuit.

  Digital Logic

  Logic Gates

  AND Gate

  NAND Gate

  OR Gate

  NOR Gate

  XOR Gate

  XNOR Gate

  Boolean Expressions

  Logic Chips

  Digital Logic

  Also known as Boolean logic, digital logic is the term used to define the concept of making extremely complicated decisions based on simple “yes/no” questions. This is the fundamental concept underpinning all modern digital circuits, software controlled devices, and computer systems.

  Simply put, it is the system of rules that allow us to design and control complex circuits. The physical part of digital logic is called the hardware; the programming part is called the software. Not all digital circuits require software to function, but they do all work on a true or false principle that can be represented by something called a truth table – more of which later.

  Digital logic is also the underlying system that drives electronic circuit board design. It also refers to the manipulation of binary values (0 or 1) using logic gates to construct circuits that can perform relatively simple tasks or highly complex multiple instructions at the speed of light, such as implemented in the operation of a computer system.

  Digital logic is a completely different aspect of electronics than that you have been learning so far. Signals have only two states: “On” or “Off”.

  Digital circuits

  Today we are surrounded by digital logic circuits, or digital circuits

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  eBook - ePub

  Electronic Logic Circuits

  • J. Gibson(Author)
  • 2013(Publication Date)
  • Routledge

    (Publisher)

  Diagrams of networks using symbols indicating only logic (e.g. dee for AND) will be referred to as logic circuit diagrams. When networks require a specific electrical component implementing a logic function the rectangular symbol will be used and the network will be referred to as an electrical circuit. Further brief comments concerning symbols are made in Appendix C. One further method which is used to describe any logic circuit is to express its behaviour in terms of Boolean algebra. This algebra is the mathematical description of systems which are only allowed to have two states and it will be examined in more detail later. An essential definition in Boolean algebra is the AND function, and in equations the function is represented by a dot. For example, the Boolean expression for a three-input AND gate is the equation R = A.B.C which is read as R equals A and B and C. 2.2.2 The OR gate This element is another one which implements a fundamental definition in Boolean algebra. The OR gate is the combinational logic circuit which has any number of inputs and has an output of 1 when any one, or more than one, of the inputs is 1. An alternative statement is that the circuit gives the output 1 unless all the inputs are 0, in which case it gives the output 0. Note that the output of a two-input OR circuit is not just 1 in the cases input A is 1 with B equals 0, or input B is 1 with A equals 0; it also includes the situation where A and B are both 1 (i.e. A is 1 or B is 1 or A and B are both 1). From this description the truth table can be constructed; Table 2.5 is that for a three-input OR gate. Table 2.5 Figure 2.4 shows some of the symbols used to represent an OR gate. Following the practice introduced for AND gate symbols the form in Fig. 2.4c represents a complete electrical OR gate unit while that in Fig. 2.4a is the symbol for a ‘pure logical’ OR function

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  eBook - ePub

  Principles of Transistor Circuits

  • S W Amos, Mike James(Authors)
  • 2000(Publication Date)
  • Newnes

    (Publisher)

  Fig. 15.4

  Fig. 15.4 ‘Curvy’ symbols used in the American Mil-Std-806

  Integrated circuit gates

  Gate circuits can be constructed of discrete components but normally they are in the form of integrated circuits. For example a single i.c. may contain three 3-input gates. To use such an i.c. in an equipment it is not necessary to know details of the circuitry of the device. All the designer needs to know to be able to use the i.c. successfully are details of input and output signal levels, polarities, impedances and supply voltages. In preparing diagrams of computers and computer-like equipments the gates and other functional units are represented by block symbols such as those given for gates in Fig. 15.3 . To help in the layout of printed wiring cards and in maintenance the inputs, outputs and supply points of the gates can be identified in the block diagram by giving the pin numbers of the i.cs. Block diagrams of logic equipment are usually known as logic diagrams.

  To illustrate the versatility of logic gates a number of applications will now be considered.

  Gates as switches

  Table 15.2 shows that when input A is at logic 0, the output is also at logic 0 (irrespective of the signal on input B ) whereas if input A is at logic 1 the output signal is the same as the signal on input B . Thus an AND gate can be used as a switch, a logic 1 signal on input A allowing the signal on input B to pass through the gate, a logic 0 signal on input A blocking the signal on input B .

  An OR gate can be used similarly but here a logic 0 on one input allows the signal on the other input to pass through the gate.

  Inverters

  Table 15.4 shows an interesting property of a NAND gate. When there is a logic 1 signal on input A the output from the gate is the inverse of that on input B . A NAND gate is frequently so used, input A being connected permanently to a source of logic 1 voltage as shown in Fig. 15.5 . For some types of NAND gate i.cs it is sufficient simply to leave input A unconnected: this has the same effect as connecting it to a logic 1 source. A gate with this property is known as a NOT gate. Another way of converting a NAND into a NOT gate (inverter) is to couple the inputs together. This is also shown in Fig. 15.5

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  eBook - ePub

  Digital Electronics

  • John Morris(Author)
  • 2013(Publication Date)
  • Routledge

    (Publisher)

  2

  Logic Gates

  ‘A logic gate is a device which can have more than one binary input but a single binary output. The state of the output is determined by the input conditions’.

  Every logic gate can be depicted as a symbol, Boolean expression and truth table. While the truth tables and Boolean expressions are universally accepted there are considerable differences in the gate symbols. In the United Kingdom logic symbols are devised by the British Standards Institute (BSI). Unfortunately however, the American standard symbols (MIL/ANSI) for logic gates have a greater following. This has now reached such a level that the BSI symbols for logic gates are being almost universally superseded by the MIL/ANSI symbols. The reason for this is probably that the American Versions are clearer and more easily understood. It is quite possible that in the not to distant future BSI symbols will be changed so that they conform to those of the MIL/ANSI. For reasons of clarity MIL symbols for logic circuits will be used throughout this book.

  Fig. 2.1  Logic symbols and Truth tables

  Fig. 2.1 shows the common logic gate symbols together with their Boolean expressions and truth tables.

  Gate Operations The gate operation can be represented by the Boolean expression and the truth table, this is summarized as follows. The inverter or NOT gate This produces an output which is the inverse or opposite of the input signal. Therefore if the input to an inverter is Logic 1 the output will be Logic 0. The OR gate A Logic 1 output is produced if any input is at Logic 1. For a gate with four inputs A, B, C, D the Boolean expression would be: Q = A + B + C + D with the plus sign (+) denoting the OR function, showing that the output Q = ‘1’ if any of the inputs A, B, C, D are at ‘1’. The NOR gate This is the inverse of the OR gate, i.e. it will give an output that is the opposite of that gate. The Boolean expression for a four input gate will be:

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  eBook - ePub

  Semiconductor Basics

  A Qualitative, Non-mathematical Explanation of How Semiconductors Work and How They are Used

  • George Domingo(Author)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  11 Logic Circuits OBJECTIVES OF THIS CHAPTER Now we are going back to talk about how we use semiconductor devices to perform useful operations. In the first two sections we'll talk about the way we interphase with the computer and the basic language we use, that is, Boolean algebra and logic symbols. Then I will explain how we implement this algebra with switches (to clear the concepts) and semiconductor devices, and we'll see how to do arithmetic operations, sums, subtractions, multiplications, and divisions with the devices we covered in the previous chapters. In the previous chapters I very much concentrated on the performance of individual components and how to use them, mainly in the analogue mode. Now we are going digital. 11.1 Boolean Algebra Everybody knows that digital computers work with 1s and 0s. Computers do not understand the number 3. All the computations that computers have to carry out to give us any meaningful results are done using the ON and OFF conditions, ON for 1 and OFF for 0. The large TV screen that give us beautiful and sharp pictures with bright colors is based on millions of points that can be ON or OFF. Each point of light consists of three miniscule LEDs of three different colors. How a computer manipulates all this data is based on the concepts of Boolean algebra. (Forget about the word algebra. There are no equations involved outside of adding and subtracting.) Mr. George Boole (1815–1864; Figure 11.1) was a British mathematician and philosopher with interest in strengthening the logic concepts. Aristotle is credited with creating logic thinking with his famous syllogisms, such as “All men are mortal, I am a man, therefore I am mortal” or, more abstractly, “All A are B, all B are C, therefore all A are C”. He wanted to be sure that people were logical and consistent in advancing any idea. What Boole did was to add mathematical formalism, symbolic logic, to Aristotle's logic

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  eBook - ePub

  Analog and Pulse Circuits

  • Dayaydi Lakshmaiah, C.B. Ramarao, K. Kishan Rao(Authors)
  • 2022(Publication Date)
  • CRC Press

    (Publisher)

  CHAPTER 6 Logic Gates

  6.1 THE AND GATE

  An AND gate has two or more inputs but only one output. AND gate is also called an all or nothing gate.

  Bellow figure shows symbols and truth tables of two-input and their input AND gates. Note that the output is 1 only when each one of the inputs is 1. The symbol for the AND operation is .or we use symbol at all. The AND operation is logical multiplication.

  Figure 6.1 Logic Symbol

   6.1 (a) Two-input AND gate With the input variables to the AND gate represented by, A, B, C...., the Boolean expression for the output can be written as X = A.B and lead as “X is equals to A and B”.

  Figure 6.2 Operation of two i/p AND gate

  A and B are mechanical switches connected in series and X is the lamp. It can be observed that the lamp X lights up only when both the switches A and B are closed. It can also be observed that the lamp does not light up with (a) both A and B open, (b) A open and B close and (c) A closed and B open. Let binary 0 indicate an open switch and binary one indicate a closed switch. Also let binary 0 indicate a dark lamp and binary 1 indicate a bright lamp. The various combinations of the switch positions and the state of the lamp are listed below.

  Switches	Lamp
  A	B	X
  Open	Open	Dark
  Open	Close	Dark
  Close	Open	Dark
  Close	Close	Bright

  Switches	Lamp
  A	B	X
  0	0	0
  0	1	0
  1	0	0
  1	1	1

  This is the same as the truth table of a two-input AND gate.

  6.2 THE NOT GATE (INVERTER)

  A NOT gate also called as an Inverter. It is a device whose output is always the complement of its input.

  Figure 6.3 Logic symbol

  Figure 6.4 Transistor inverter

  REALIZATION OF NOT GATE

  1. When A = 0 V, transistor T is OFF, NO current flows through R and hence no voltage drop occurs across R. The output voltage X = +5 V.
  2. When A = +5 V, T is ON. Current flows through R and hence almost all the supply voltage is dropped across R.

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