EBK COMPUTER SCIENCE ILLUMINATED
EBK COMPUTER SCIENCE ILLUMINATED
7th Edition
ISBN: 9781284174755
Author: Dale
Publisher: JONES+B CO
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Chapter 4, Problem 35E

Explanation of Solution

Gates:

  • A gate is a device which is used to perform the basic logical operation.
  • It accepts one or more input signals and generates single output signal.
  • It contains several types of gates.
  • Six types of gates are most commonly used. They are:
    • NOT gate
    • AND gate
    • OR gate
    • XOR gate
    • NAND gate
    • NOR gate
  • NOT gate:
    • A NOT gate accepts only one input value to generate single output value.
    • When the input is 0, then the output is 1. The output of the NOT gate is the inversion of its input.
    • So, it is also referred to as inverter.
    • It is represented in three ways:
      • In “Boolean expression”, the NOT operation is expressed using the “'” mark or “¯” horizontal bar symbol.

  X = A'     or      X = A¯

Where A is the input and X is the output.

  • The “logic diagram” for NOT gate takes A as input and generates a single X as output:

EBK COMPUTER SCIENCE ILLUMINATED, Chapter 4, Problem 35E , additional homework tip  1

  • The “Truth table” for the NOT gate:
AX = A¯
01
10
  • AND gate:
    • An AND gate accepts two inputs and generates a single output.
    • When both the inputs are 1, then the output is 1. Otherwise, the output is 0.
    • It is represented in three ways:
      • In “Boolean expression”, the AND operation is expressed using the “.” dot operator or “*” asterisk operator.

  X = A  B     or      X = A * B

Where A and B are the inputs and X is the output.

  • The “logic diagram” for AND gate takes two inputs and generates a single output:

EBK COMPUTER SCIENCE ILLUMINATED, Chapter 4, Problem 35E , additional homework tip  2

  • The “Truth table” for the AND gate:
ABX = A  B
000
010
100
111
  • OR gate:
    • An OR gate accepts two inputs and generates a single output.
    • When both the inputs are 0, then the output is 0. Otherwise, the output is 1.
    • It is represented in three ways:
      • In “Boolean expression”, the OR operation is expressed using the “+” plus sign.

        X=A+B

     Where A and B are the inputs and X is the output.

  • The “logic diagram” for OR gate takes two inputs and generates a single output:

EBK COMPUTER SCIENCE ILLUMINATED, Chapter 4, Problem 35E , additional homework tip  3

  • The “Truth table” for the OR gate:
ABX=A+B
000
011
101
111
  • XOR gate:
    • An XOR gate accepts two inputs and produces a single output.
    • When both the inputs are same, then the output is 0. Otherwise, the output is 1.
    • It is represented in three ways:
      • In “Boolean expression”, the XOR operation is expressed by using the “” symbol.

        X = A  B

  Where A and B are the inputs and X is the output.

  • The “logic diagram” for XOR gate takes two inputs and generates a single output:

EBK COMPUTER SCIENCE ILLUMINATED, Chapter 4, Problem 35E , additional homework tip  4

  • The “Truth table” for the XOR gate:
ABX = AB
000
011
101
110
  • NAND gate:
    • The NAND gate accepts two inputs and produces a single output.
    • It produces the opposite results of an AND gate.
    • If both the inputs are 1, then the output is 0. Otherwise, the output is 1.
    • It is represented in three ways:
      • The “Boolean expression” for NAND gate:
        • No specific symbol is used to express the NAND operation.
        • The expression for NAND is the negation of an AND operation.

X = (A · B)'  or   X = (A · B)¯

  Where A and B are the inputs and X is the output.

  • The “logic diagram” for NAND gate:
    • It takes two inputs and generates a single output.

EBK COMPUTER SCIENCE ILLUMINATED, Chapter 4, Problem 35E , additional homework tip  5

  • The “Truth table” for the NAND gate:
ABX = (A · B)¯
001
011
101
110
  • NOR gate:
    • The NOR gate accepts two inputs and produces a single output.
    • It produces the opposite results of an OR gate.
    • If both the inputs are 0, then only the output is 1. Otherwise, the output is 0.
    • It is represented in three ways:
      • In “Boolean expression”,
        • No specific symbol is used to express the NOR operation.
        • The expression for NOR is the negation of an OR operation.

          X = (A + B)' or X = (A + B)¯

  Where A and B are the inputs and X is the output.

  • The “logic diagram” for NOR gate takes two inputs and generates a single output:

EBK COMPUTER SCIENCE ILLUMINATED, Chapter 4, Problem 35E , additional homework tip  6

  • The “Truth table” for the NOR gate:
ABX = (A + B)¯
001
010
100
110

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