Chapter 5, Problem 30RE

a.

Program Plan Intro

AND gate:

• The “AND” gate refers to a logic gate whose output will be “HIGH” which means “1” only, when all the inputs are “HIGH”.
• The output of “AND” gate will be “LOW” which means “0”, when any one of its input will be “LOW”.
• The truth table for “AND” gate is as follows:

A	B	$Y=A\&\&B$
0	0	0
0	1	0
1	0	0
1	1	1

• “AND” operation can be denoted by “&&”.

OR gate:

• The “OR” gate refers to a logic gate whose output will be “HIGH” when any one of the inputs or both is “HIGH”.
• The output of “OR” gate will be “LOW” when both the inputs will be “LOW”.
• The truth table for “OR” gate is as follows:

A	B	$Y=A\left|\right|B$
0	0	0
0	1	1
1	0	1
1	1	1

• “OR” operation can be denoted by “||”.

NOT gate:

• It accepts only one input value to produce the single output value.
• If the input is “0”, then the output is “1”.
• The output is the inversion of the input. So, it is also referred to as an inverter.
• The truth table for the “NOT” gate is as follows:

A	$X=\overline{A}$
0	1
1	0

• “NOT” operation can be denoted by “!”.

b.

Explanation of Solution

Simplification of expression:

• Given,
  • The value of “b” is “false”.
  • The value of “x” is “0”.
• The given expression is “$b\left|\right|x==0$”
• Here, “$x==0$”
• Thus, the value of “x” can be termed as “true”.
• It can be stated that both are having different values such as, “false” for “b” and “true” for “x”

c.

Explanation of Solution

Simplification of expression:

• Given,
  • The value of “b” is “false”.
  • The value of “x” is “0”.
• The given expression is “$!b\&\&x==0$”
• Here, “$x==0$”
• Thus, the value of “x” can be termed as “true”.
• The symbol “!” represents “NOT”.
• Thus, the value of “b” changes from “false” to “true”

d.

Explanation of Solution

Simplification of expression:

• Given,
  • The value of “b” is “false”.
  • The value of “x” is “0”.
• The given expression is “$!b\left|\right|x==0$”
• Here, “$x==0$”
• Thus, the value of “x” can be termed as “true”.
• The symbol “!” represents “NOT”.
• Thus, the value of “b” changes from “false” to “true”

e.

Explanation of Solution

Simplification of expression:

• Given,
  • The value of “b” is “false”.
  • The value of “x” is “0”.
• The given expression is “$b\&\&x!=0$”
• Here, “$x!=0$”
• The symbol “!” represents “NOT”.
• Thus, the value of “x” changes from “true” to “false”

f.

Explanation of Solution

Simplification of expression:

• Given,
  • The value of “b” is “false”.
  • The value of “x” is “0”.
• The given expression is “$b\left|\right|x!=0$”
• Here, “$x!=0$”
• The symbol “!” represents “NOT”.
• Thus, the value of “x” changes from “true” to “false”

g.

Explanation of Solution

Simplification of expression:

• Given,
  • The value of “b” is “false”.
  • The value of “x” is “0”.
• The given expression is “$!b\&\&x!=0$”
• The symbol “!” represents “NOT”.
• Thus, the value of “b” changes from “false” to “true”.
• Here, “$x!=0$”
• Thus, the value of “x” changes from “true” to “false”

h.

Explanation of Solution

Simplification of expression:

• Given,

  The value of “b” is “false”.

  The value of “x” is “0”.

• The given expression is “$!b\left|\right|x!=0$”
• The symbol “!” represents “NOT”.
• Thus, the value of “b” changes from “false” to “true”.
• Here, “$x!=0$”
• Thus, the value of “x” changes from “true” to “false”