Chapter 3, Problem 24E

a.

Program Plan Intro

NOT operation:

• NOT function needs one input and produces one output.
• It is also known as unary logical function.
• Another name of NOT operation is complementary operation.
• Output is produced by complementing the input.
• The following diagram depicts the NOT operation,

• The NOT operation produces the output “1”, when the source input is “0”.
• The NOT operation produces the output “0”, when the source input is “1”.
• The truth table for the NOT operation is as follows,

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

• In the above table, “X” is the input, and “Z” is the output.
• When “X=0”, the output “Z” is the complement of “0”, which means “1” and When “X=1”,the output “Z” is the complement of “1”, which means “0”.

OR operation:

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

• The truth table for OR operation is as follows,

X	Y	Z=X OR Y
0	0	0
0	1	1
1	0	1
1	1	1

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

AND function:

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

• 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

• 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”.

b.

Explanation of Solution

Function to be implemented for the given criteria:

• Truth table to implement the function “F”, which has the value “1” only when the value of “A” is “1” and the value of “B” is “0” is as follows,

Inputs		Output
A	B	F
0	0	0
0	1	0
1	0	1
1	1	0

K-Map:

The K-map for the above truth table is as follows,

c.

Explanation of Solution

Function to be implemented for the given criteria:

• The given truth table for the one-bit adder is as follows,

Inputs		Output
A	B	Sum
0	0	0
0	1	1
1	0	1
1	1	0

K-Map:

The K-map for the above truth table is as follows,

d.

Explanation of Solution

Creation of four-bit adder:

“No”, it is not possible to make a four-bit adder.

Explanation:

• The logic diagram derived in part “c” is a half adder.
• The logic circuit needs four full adder circuits to implement four-bit adder.
• Therefore, using four copies of logic diagram derived in part “c”, it is not possible to make a four-bit adder.

Missing information:

• Carry information is missing in the given truth table...