Chapter 2, Problem 30E

a.

Program Plan Intro

AND function:

• AND function needs two inputs and produces one output.
• It is also known as binary logical function.
• If either of the inputs or both the inputs are “0”, then one-bit AND operation produces the output as “0”.
• If both inputs are “1”, then AND operation produces the output as “1”.
• The following diagram depicts the AND operation,

b.

Explanation of Solution

101 AND 110:

The truth table for AND operation is as follows,

X	Y	X AND Y
0	0	0
0	1	0
1	0	0
1	1	1

Explanation for the truth table:

• In the above table, “X” and “Y” are inputs, and “Z” is output.
• When “X=0”, and “Y=0”, the output is “0”, because both the inputs “X” and “Y” contains the value “0”.
• When “X=0”, and “Y=1”, the output is “0”, because one of the input “X” contains the value “0”.
• When “X=1”, and “Y=0”, the output is “0”, because one of the input “Y” contains the value “0”...

c.

Explanation of Solution

11100000 AND 10110100:

The truth table for AND operation is as follows,

X	Y	X AND Y
0	0	0
0	1	0
1	0	0
1	1	1

Explanation for the truth table:

• In the above table, “X” and “Y” are inputs, and “Z” is output.
• When “X=0”, and “Y=0”, the output is “0”, because both the inputs “X” and “Y” contains the value “0”.
• When “X=0”, and “Y=1”, the output is “0”, because one of the input “X” contains the value “0”.
• When “X=1”, and “Y=0”, the output is “0”, because one of the input “Y” contains the value “0”...

d.

Explanation of Solution

00011111 AND 10110100:

The truth table for AND operation is as follows,

X	Y	X AND Y
0	0	0
0	1	0
1	0	0
1	1	1

Explanation for the truth table:

• In the above table, “X” and “Y” are inputs, and “Z” is output.
• When “X=0”, and “Y=0”, the output is “0”, because both the inputs “X” and “Y” contains the value “0”.
• When “X=0”, and “Y=1”, the output is “0”, because one of the input “X” contains the value “0”.
• When “X=1”, and “Y=0”, the output is “0”, because one of the input “Y” contains the value “0”...

e.

Explanation of Solution

(0011 AND 0110) AND 1101:

The truth table for AND operation is as follows,

X	Y	X AND Y
0	0	0
0	1	0
1	0	0
1	1	1

Explanation for the truth table:

• In the above table, “X” and “Y” are inputs, and “Z” is output.
• When “X=0”, and “Y=0”, the output is “0”, because both the inputs “X” and “Y” contains the value “0”.
• When “X=0”, and “Y=1”, the output is “0”, because one of the input “X” contains the value “0”.
• When “X=1”, and “Y=0”, the output is “0”, because one of the input “Y” contains the value “0”.
• When “X=1”, and “Y=1”, the output is “1”, because both the inputs “X” and “Y” contains the value “1”...

f.

Explanation of Solution

0011 AND (0110 AND 1101):

The truth table for AND operation is as follows,

X	Y	X AND Y
0	0	0
0	1	0
1	0	0
1	1	1

Explanation for the truth table:

• In the above table, “X” and “Y” are inputs, and “Z” is output.
• When “X=0”, and “Y=0”, the output is “0”, because both the inputs “X” and “Y” contains the value “0”.
• When “X=0”, and “Y=1”, the output is “0”, because one of the input “X” contains the value “0”.
• When “X=1”, and “Y=0”, the output is “0”, because one of the input “Y” contains the value “0”.
• When “X=1”, and “Y=1”, the output is “1”, because both the inputs “X” and “Y” contains the value “1”...