Chapter 3, Problem 29E

Program Plan Intro

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”.

NOR function:

• The NOR operation produces the output which is the negation of the result of “OR” operation.
• If one or both the inputs are “1”, then NOR operation produces the output as “0”.
• If both the inputs are “0”, then NOR operation produces the output “1”.
• The following diagram depicts the NOR operation,

• The truth table for NOR operation is as follows,

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

NAND function:

• The NAND operation produces the output which is the negation of the result of “AND” operation.
• If one or both the inputs are “0”, then NAND operation produces the output “1”.
• If both inputs are “0”, then NAND operation produces the output as “0”.
• The following diagram depicts the NAND operation,

• The truth table for NAND operation is as follows,

X	Y	X NAND Y
0	0	1
0	1	1
1	0	1
1	1	0