Logic Gate Diagrams

11 Key excerpts on "Logic Gate Diagrams"

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  The Silicon Web

  Physics for the Internet Age

  • Michael G. Raymer(Author)
  • 2009(Publication Date)
  • CRC Press

    (Publisher)

  A logic operation is an elementary rule for arriving at a logical outcome. Three basic opera-tions that can serve as building blocks for all logic operations are NOT, AND, and OR. In considering complex situations, a diagram is useful to help visualize the logic process. Think of this as a flow chart for making a decision. If you face a complicated decision, such as which college to attend, there might be many factors to consider. Let us say that college B is a better school academically. Your rules for making a decision are: If college B offers you a scholarship, or if college B’s dorms have DSL lines (high-speed Internet connections), then you would attend B. However, if college A offers you a schol-arship, but not college B, and if college B’s dorms do not have DSL, then you would attend A. If neither A nor B offers a scholarship or DSL, then you would choose neither. A flow chart for this decision is shown below in Figure 6.1 . The particular case illus-trated is indicated by the circled data. You should read the logic diagram from left to right. Input information, made up of bits, “flows” along the three lines entering the diagram on the left, and output informa-tion flows to the right along the lines labeled “Attend College B?” or “Attend College A?” Each bit travels along a line until it enters a box containing a logic operation, from which an output emerges. A solid black dot on a line shows a point where information Digital Electronics and Computer Logic 189 is sent from one input source to two logic boxes. A place where two lines cross without a black dot is a bypass (like an automobile overpass); there is no exchange of informa-tion at these line crossings. It is common to refer to the lines transmitting the inputs and outputs of the boxes as wires, and to the operations inside the boxes as logic gates . In the case shown in the figure, the upper two inputs equal No and the bottom input equals Yes.

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  Principles Of Computer Programming NQF3 SB

  TVET FIRST

  • S Sasti D Sasti(Author)
  • 2019(Publication Date)
  • Macmillan

    (Publisher)

  There are 8 columns, C1–C8. l After reading the decision table, we can see that, based on 8 sequences of inputs represented by the columns, we will get only four 1s or Yes or On results. l The final result is represented in row 8. Unit 1.5: Logic gates 1.5.1 Logic gates A computer is an electronic device made up of electronic circuits that perform different actions. A logic gate is the building block of these circuits. Logic gates are devices that are based on the logical operators we studied in previous units. We can now take a Boolean expression and express it diagrammatically in the form of a logic circuit. We use symbols to represent the different gates. Table 1.9 shows the symbols and truth tables for the various logic gates. Table 1.9: Logic gate symbols and truth tables Logic gate Symbol Truth table NOT gate A Q A Q 0 1 1 0 AND gate A Q B Inputs Outputs A B Q = A AND B 0 0 0 0 1 0 1 0 0 1 1 1 11 Module 1 Logic gate Symbol Truth table OR gate A Q B Inputs Outputs A B Q = A OR B 0 0 0 0 1 1 1 0 1 1 1 1 NAND gate A Q B Inputs Outputs A B Q = A NAND B 0 0 1 0 1 1 1 0 1 1 1 0 NOR gate A Q B Inputs Outputs A B Q = A NOR B 0 0 1 0 1 0 1 0 0 1 1 0 Exclusive OR (XOR) gate A Q B Inputs Outputs A B Q = A XOR B 0 0 0 0 1 1 1 0 1 1 1 0 The new logical operators in Table 1.9 are the NAND, NOR and XOR operators: l NAND: Represents NOT AND. It evaluates the inputs with the AND operator and then reverses the result. l NOR: Represents NOT OR. It evaluates the inputs with the OR operator and then reverses the result. l XOR: We will discuss the XOR operator in the next section. Each gate may have two or more inputs, except for the NOT gate (inverter) which works on a single input. The logic gate symbols for the negating operators (NOT, NOR, NAND) have a small circle at the end of the gate. 12 Topic 1 Example 1.6: Designing logic circuits from Boolean expressions Draw the circuit for the following Boolean expressions: 1.

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  Digital Electronics

  Principles, Devices and Applications

  • Anil K. Maini(Author)
  • 2007(Publication Date)
  • Wiley

    (Publisher)

  Each one of the basic logic gates is a piece of hardware or an electronic circuit that can be used to implement some basic logic expression. While laws of Boolean algebra could be used to do manipulation with binary variables and simplify logic expressions, these are actually implemented in a digital system with the help of electronic circuits called logic gates. The three basic logic gates are the OR gate, the AND gate and the NOT gate. 4.3.1 OR Gate An OR gate performs an ORing operation on two or more than two logic variables. The OR operation on two independent logic variables A and B is written as Y = A + B and reads as Y equals A OR B and not as A plus B . An OR gate is a logic circuit with two or more inputs and one output. The output of an OR gate is LOW only when all of its inputs are LOW. For all other possible input combinations, the output is HIGH. This statement when interpreted for a positive logic system means the following. The output of an OR gate is a logic ‘0’ only when all of its inputs are at logic ‘0’. For all other possible input combinations, the output is a logic ‘1’. Figure 4.3 shows the circuit symbol and the truth table of a two-input OR gate. The operation of a two-input OR gate is explained by the logic expression Y = A + B (4.1) As an illustration, if we have four logic variables and we want to know the logical output of ( A + B + C + D , then it would be the output of a four-input OR gate with A , B , C and D as its inputs. Y=A+B A B A 0 0 1 1 B 0 1 0 1 Y 0 1 1 1 Figure 4.3 Two-input OR gate. 72 Digital Electronics Y=A+B+C A B C (a) Y=A+B+C+D A C (b) D A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 Y 0 1 1 1 1 1 1 1 (c) B Figure 4.4 (a) Three-input OR gate, (b) four-input OR gate and (c) the truth table of a three-input OR gate. Figures 4.4(a) and (b) show the circuit symbol of three-input and four-input OR gates. Figure 4.4(c) shows the truth table of a three-input OR gate.

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  Embedded Systems Circuits and Programming

  • Julio Sanchez, Maria P. Canton(Authors)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  Chapter 3 Logic Gates and Circuit Components 3.1  Logic Gates

  A logic gate can be a virtual or a physical device. In either case the logic gate takes one or more binary signals as input and produces a binary output as a logical function. The basic logical operations of AND, OR, XOR, and NOT are described in basic electronics and Boolean algebra texts. Although logic gates can be made from electromagnetic relays, mechanical switches, or optical components, nowadays they are normally implemented using diodes and transistors.

  Charles Babbage’s Analytical Engine, devised around 1837, used mechanical logic gates based on gears. Electromagnetic relays were later used for logic gates, and these were eventually replaced by vacuum tubes, as Lee De Forest’s modification of the Fleming valve can be used as an AND logic gate. In 1937, Claude E. Shannon wrote a thesis paper that introduced the use of Boolean algebra in the analysis and design of switching circuits. The first modern electronic gate was invented by Walther Bothe in 1924, for which he received part of the 1954 Nobel prize in physics.

  The primitive types of gate are the AND, OR, and NOT. Additionally, the XOR gate offers an alternative version of the OR. All other Boolean operations can be implemented by combining the three primitive types. However, for convenience, other secondary types have been developed. These are called NAND (NOT plus AND), NOR (NOT plus OR), and XNOR (XOR plus NOT). The advantage of these secondary logic gates is that they require fewer circuit elements for a given function. In fact, the NAND gate is the simplest of all gates, except for the NOT gate. Furthermore, a NAND can implement both a NOT and an OR function; therefore it can replace AND, OR, and NOT. This means that the NAND gate is the only type actually needed in a real system. Programmable logic arrays will very often contain nothing but NAND gates. The symbols for logic gates are shown in Figure 3-1

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  Electricity and Electronics for Renewable Energy Technology

  An Introduction

  • Ahmad Hemami(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  23.2 Logic Gates A number of basic circuits, called logic gates , define the fundamental ele-ments of logic circuits. These are AND, OR, NOR, NOT, XOR, and NAND. Pay attention to the fact that often a required condition can be expressed in two ways using opposite statements but leading to the same meaning. For instance, if for the correct execution of a process the temperature needs to be above 60°, the statement for this condition can be one of the following: The temperature must be above 60° or equivalently The temperature must NOT be below 60°. As mentioned in Chapter 22, for all signals used for binary applications and bit setting the terms high and low are used. These two refer to two values that are opposite to each other. On the basis of the application they can represent true and false . The result of action of a logic gate is always expressed in the form of true or false. The practical application of it is almost always in the form of a voltage. The output of a logic gate is represented by two voltages that are used to define a distinct difference between 0 and 1. On the basis of the hardware used (e.g., type of transistor), high can be represented by zero voltage and low by a nonzero voltage. Throughout the chapter, when necessary, we assume true to be high and represented by 1, and false to be low and denoted by 0. When using transistors, the voltage difference between high and low is nominally 5 V. But, in practice, anything below 1 V is acceptable as 0 V and anything above 3 V is considered to represent 5 V. The value of 0 and Boolean algebra: Number of rules (dif-ferent from regular algebra rules) for logic gates and logic circuits. Logic gates: Number of special electronic devices exhibiting switching properties according to Boolean algebra. Logic Circuits and Applications 677 5 V for the lower and upper ends of the spectrum is an accepted standard value for transistor-transistor logic interface and is normally addressed TTL .

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  Hardware and Computer Organization

  • Arnold S. Berger(Author)
  • 2005(Publication Date)
  • Newnes

    (Publisher)

  The gate is an electronic switching circuit that implements the logical AND function for the two input values A and B. Signals travel through this region very quickly on their way up or down, but don't dwell there. If a logic value were to be measured in this region, there would be an electrical fault in the circuit. The logical function of Figure 2.2 can be described in several equivalent ways: • IF A is TRUE AND B is TRUE THEN C is TRUE • IF A is HIGH AND B is HIGH THEN C is HIGH • IF A is 1 AND B is 1 THEN C is 1 • IF A is ON AA^D B is ON THEN C is ON • IF A is 5 volts AND B is 5 volts THEN C is 5 volts The last bullet is a Uttle iffy because we allow the values to exist in ranges, rather than absolute numbers. It's just easier to say 5 volts instead of a range of 3 to 5 volts. As we've discussed in the last chapter, in a real circuit, A and B are signals on individual wires. These wires may be actual wires that are used to form a circuit, or they may be extremely fine cop-per paths (traces) on a printed circuit (PC) board, as in Figure 1.11, or they may be microscopic paths on an integrated circuit. In all cases, it is a single wire conducting a digital signal that may take on two digital values: 0 or 1. '^Assuming that we are using the older 5-volt logic families, rather than the newer 3.3-volt families. 30 Introduction to Digital Logic The next point that we want to consider is why we call this circuit element a gate. You can imagine a real gate in front of your house. Someone has to open the gate in order to gain entrance. The AND gate can be thought of in exactly the same way. It is a gate for the passage of the logical signal. The previous buUeted statements describe the AND gate as a logic statement. However, we can also describe it this way: « IF Ais 1 THENCEQUALSB • IF Ais 0 THEN C EQUALS 0 Of course, we could exchange A and B because these inputs are equivalent.

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  N4 Logic Systems

  • B Schrickker, B Madaramoothoo, B Schrickker, B Madaramoothoo(Authors)
  • 2013(Publication Date)
  • Future Managers

    (Publisher)

  In digital engineering, we use Boolean algebra as the ‘mathematics’ to determine how logic circuits function under various conditions. It is imperative that a recap of logic circuits such as the NOT, OR, AND, NAND, XOR and NOR gates, is completed as this unit will take that knowledge further. AND Gate In Figure 3.1, the AND gate symbol, truth table and switching circuit are represented below: A B & X 5 A.B A B X 1 5 v 0 v A B X 0 0 0 0 1 0 1 0 0 1 1 1 Symbol Truth Table Switching Circuit Figure 3.1 From the switching circuit and truth table it can be seen that for Lamp X to burn, both Switch A and B must a high or 1. Any other condition for this two-input circuit will result in the lamp not burning. OR Gate In Figure 3.2, the OR gates Symbol, Truth Table and Switching Circuit can be seen. A B  1 X 5 A 1 B A B X 0 0 0 0 1 1 1 0 1 1 1 1 A B X 1 5 v 0 v Symbol Switching Circuit Truth Table Figure 3.2 As can be seen from the above truth table, the OR gate produces a result of 1 when any of the inputs (A or B) is 1. Furthermore, the OR gate produces an output result of 0 only if all the inputs are 0. 59 N4 Logic Systems| Hands-On! NOT Gate The NOT gate seen in Figure 3.3 above, only has one input. The output of the NOT gate can therefore only have two possible values, namely, “1” or “0”. The NOT gate is also known as an inverter due to the fact that it complements or “inverts” its input. A ​ __ A ​ NOT gate A __ A 0 1 1 0 Symbol Truth Table Figure 3.3 NAND Gate The NAND Gate as can be seen in Figure 3.4 above is also known as a universal gate, as it can be used in different combinations to function as any other gate. In Figures 3.5, 3.6 and 3.7 the NAND gate is configured as a NOT, OR and NOR gate respectively. A B & X 5 ​ ____ A.B ​ 2-INPUT NAND A B X 0 0 1 0 1 1 1 0 1 1 1 0 Symbol Truth Table Figure 3.4 A ​ __ A ​ A B ​ __ A ​ ​ __ B ​ A 1 B Figure 3.5 Figure 3.6

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  Computers and Microprocessors

  Made Simple

  • George H. Olsen, Ian Burdess(Authors)
  • 2016(Publication Date)
  • Made Simple

    (Publisher)

  They are being used increasingly in consumer products, such as washing machines, sewing machines, toys and television games as well as scientific applications for data acquisition and control. This shift away from the traditional markets has, to a large extent, been due to the evolution and development of the basic logic gates used in their construction. Unlike analogue systems, the digital computer is constructed entirely of switching devices capable of assuming only two states, ON and OFF. As the demands for computers have grown and new markets have opened up, the semiconductor device manufacturers have responded by increasing the speed and reducing the size of the basic logic circuits. A majority of the systems in use today is now based upon the popular transistor-transistor logic (TTL) NAND gate. By using these TTL NAND gates, it is possible to design and construct a logic circuit capable of making decisions based upon the current state of the input signals. These combinational logic circuits may be used to perform such elementary tasks as checking the door interlocks of an automatic washing machine before the wash cycle starts, or they may be used to construct a com-plex and high-speed arithmetic unit of a computer capable of adding numbers together at the rate of hundreds of thousands per second. Combinational logic circuits are, however, incapable of learning by experi-ence and always respond to a given situation in exactly the same manner. Based upon the same TTL NAND gates, but by incorporating feedback, it is possible to construct a circuit which can take into account its past experience. These systems, referred to as sequential logic systems, are very important in computers as they can be used to store information and count events as they occur. Finally, at the centre of any computer is a unit which is capable of perform-ing arithmetic calculations at very high speed.

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  Apple I Replica Creation

  Back to the Garage

  • Tom Owad(Author)
  • 2005(Publication Date)
  • Syngress

    (Publisher)

  Using logic expressions, DeMorgan's Laws, and Boolean algebra, you can quickly sketch out basic circuits on paper or even in a simple text editor. Logic expressions will allow you to show gates and lines with symbols and letters. DeMorgan's Laws will allow you to swap gates to get more efficient circuits. Boolean algebra will allow you to simplify your circuits. Logic Expressions Ambiguities in the English language can make it very difficult to precisely express digital logic; there- fore, an algebra has been developed for this purpose. Understanding this algebra is merely a matter of getting accustomed to the symbols. Table 3.10 displays these symbols, listed in order of precedence. www.syngress.com Digital Logic 9 Chapter 3 61 Table 3.10 Algebraic Symbols for Expressing Digital Logic Symbol Meaning NOT 9 AND + OR XOR Figure 3.30 shows a few logic expressions and their equivalent circuits. Take a good look at these and make sure you understand them. Try writing a few of your own. Figure 3.30 Logic Expressions F=AoB #I 7408 A 1[---,)3 F A B 2 B F-A'+ +e #9 7404 #2 74g~2 F=A ~B' #3 7486 A #107404 I ~[._...~~~:, 3 B 1[~ 2 F(A 9 B)' #4 7400 2 F-A,B+C #5 7408 A 1 I ~ ~ #6 7432 B 2 ~ 1 ~ 3 2 C I F-Ao (B+ C) #77432 2 #il 74O8 I F=[A+(B ~C)]oD A #127432 I . #11 7486 J i ~ C 2 #137408 'E) 2 3 F 62 Chapter 3 9 Digital Logic DeMorgan's Laws The term DeMorgan's Laws sounds dull and tedious, but these laws are a real boon for the improvising hacker. DeMorgan's laws explain how we can substitute different combinations of gates to best use our available resources. They can be expressed as: (A+ B)' = A' oB' (AoB)'=A'+B' Let's take (A 9B) ' (a NAND gate), for example. This statement means that A and B are not both true; therefore, at least one of them is false. Consequently, it follows that A is not true or B is not true, which we can write as A' + B'. This looks like a slight change from the first equation, but it can make a huge difference.

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  Essentials of Electrical and Computer Engineering

  • J. David Irwin, David V. Kerns, Jr.(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  CHAPTER 12 Digital Electronics and Logic Circuits LEARNING OBJECTIVES • To understand the binary number system • To learn to use Boolean algebra and its role in logic function minimization • To understand the types and operations of basic logic gates • To learn to realize NAND gates with both NMOS and CMOS devices • To learn to analyze and design combinational logic circuits • To learn to analyze and design sequential logic circuits INTRODUCTION Digital electronics is having, and will continue to have, a profound effect on vast areas of techno- logical development. In communications alone, the tentacles of this technology have permeated essentially every possible facet of this area. Only a cursory examination of the growth of cell phones around the world is sufficient to see the effect this technology is having on the lives of everyone. The Internet, which is a high-speed digital communication pipe, has made us aware of events all around the world in seconds of the time in which they have occurred. The processing speed of our computers, which is directly related to the advances in digital electronics, continues to increase at a phenomenal rate. Digital logic circuits, which form the backbone of the digital communication and processing systems, are driven by electronics that operate in a discrete mode. We saw in the last chapter that two of the transistor’s operating states are saturation and cutoff. While these operating states are not used in analog amplifiers, they are the building blocks for digital systems. In saturation, the output voltage of the transistor is low, and in cutoff the output voltage is high. We can then associate the high voltage with a logic state of 1 and the low voltage with a logic state of 0. The blazing speed of transistors permits us to shift from one state to another in the design of high-speed digital circuits. THE BINARY NUMBER SYSTEM The number of digits employed in any number system is called the base or radix.

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  Reeds Vol 10: Instrumentation and Control Systems

  • Gordon Boyd, Leslie Jackson(Authors)
  • 2013(Publication Date)
  • Thomas Reed

    (Publisher)

  Note : In logic circuitry entire circuits are packaged and it is not necessary to know the exact circuit configuration of a particular device (chip) because it is encapsulated. Signal tracing is impossible and it is only necessary to understand the relation between overall input and output signals and repair is by replacement (the black box philosophy). NAND and NOR are obviously combinations of the three given actions and various ‘tree’ type circuits can be quickly built up for otherwise complicated functions. For example, the logic illustrative circuit shown as a combination in Figure 16.13. The circuit may be interpreted as follows: ‘if the off signal is not interrupted at the button 1 2 Off On A D E F G H B C AND OR NOT 1 2 3 3 Figure 16.13 ▲ Logic units Logic and Computing • 297 and the on signal or the feedback (or interlock) signal G is energised there will be an output at H. Pressing the on button gives inputs at A and D, hence an AND function and output at H (the two NOT functions at B and C cancel, that is, like two negatives make a positive; similarly E and F). Release of the on button still allows output to be maintained through the feedback, that is, the alternative input of the two element (OR) circuit. Pressing the off button cuts off one of the signals in the AND circuit and cuts off output H. Strictly the combined sketch is NOT (A), NOR ( D ), NAND (CF) but redundant items (BCEF) simplify to OR (D) and AND (CF) and the shading section on D would then be crossed. Flip-flop circuit Multi-vibrator circuits have been discussed in Chapter 7. The univibrator circuit as sketched in symbolic form in Figure 16.14 is used in computers. With inputs X and Y at state 1, say –6 V, the feedbacks at state 0 (0 V) and state 1 (–6 V). For the lower gate feedback (0) and input Y (1) through NAND gives state 1 (–6 V). For the upper gate feedback (1) and input X (1) through NAND gives state 0 (0 V). Connecting inputs to state 0 will give stable reversing.

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