COMPUTER SCIENCE ILLUMIN.-TEXT
COMPUTER SCIENCE ILLUMIN.-TEXT
7th Edition
ISBN: 9781284156010
Author: Dale
Publisher: Jones & Barlett
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Chapter 4, Problem 43E

Explanation of Solution

Three-input AND gate:

  • AND gate:
    • The AND gate performs the multiplication of its inputs.
    • It can accept more than two inputs and performs the product of its inputs to generate the output value.
    • The output of AND gate is nothing but the product of its input values.
  • Boolean expression:
  • Boolean expression is a form of mathematical notation to express the processing of gates.
  • The Boolean expression that is used to represent the processing of three input AND gate is:

X=· B · C

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

  • Truth table:
  • Truth table is a table that contains all possible inputs and the equivalent output values to express the processing of gates.
  • Truth table for three-input AND gate is shown below:
ABCX=· B · C
0000
0010
0100
0110
1000
1010
1100
1111
  • In the above truth table:
    • When all the inputs are 0, then it generates the output as 0.

  X=· 0 · 0=· 0=0

  • When the inputs are A as 0, B as 0, and C as 1 then it generates the output as 0.

  X = 0 · 0 · 1 = 0 · 1 = 0

  • When the inputs are A as 0, B as 1, and C as 0 then it generates the output as 0

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