COMPUTER SCIENCE ILLUMIN.-TEXT
COMPUTER SCIENCE ILLUMIN.-TEXT
7th Edition
ISBN: 9781284156010
Author: Dale
Publisher: Jones & Barlett
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Chapter 4, Problem 40E

Explanation of Solution

Three ways to represent an NAND gate:

  • A gate is a device which is used to perform the basic logical operation.
  • It accepts one or more input signals and produces the single output signal.
  • It contains the three types of methods to represent the processing of gates. They are:
    • Boolean expressions
    • Logic diagrams
    • Truth tables
  • It contains several types of gates. The most common types are:
    • NOT gate
    • AND gate
    • OR gate
    • XOR gate
    • NAND gate
    • NOR gate
  • NAND gate:
    • An NAND gate 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.

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

  • The “Truth table” for the NAND gate:
ABX = (A · B)¯
001
011
101
110
  • From the above truth table:
    • When both the inputs are 0, then the output is 1

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