Chapter 4, Problem 44E

Explanation of Solution

Three-input OR gate:

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

$\text{X}=\text{A}+\text{B}+\text{C}$

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 OR gate is shown below:

A	B	C	$\text{X}=\text{A}+\text{B}+\text{C}$
0	0	0	0
0	0	1	1
0	1	0	1
0	1	1	1
1	0	0	1
1	0	1	1
1	1	0	1
1	1	1	1

• In the above truth table:
• When all the inputs are 0, then it generates the output as 0.

  $\text{X}=\text{0}+\text{0}+\text{0}=\text{0}+\text{0}=\text{0}$

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

  $\text{X}=\text{0}+\text{0}+\text{1}=\text{0}+\text{1}=\text{1}$

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