Chapter 2, Problem 34E

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

To compute “NOT (1000 AND (1100 OR 0101))”:

• To compute “(1100 OR 0101)”,
  • The OR operation can be applied on each pair of bits individually and hence it is called bit-wise OR operation.
  • The OR operation for the binary numbers “1100” and “0101” is as follows,

• The output bit is “1”, when one or both of the input bits are “1” and the output bit is “0”, when both the input bits are “0”.
• The result of “(1100 OR 0101)” is “1101”.
• To compute “1000 AND (1100 OR 0101))”,
• Compute the AND operation for the binary number “1000” and the result “1101”.
• The AND operation can be applied on each pair of bits individually and hence it is called bit-wise AND operation.
• The AND operation for the given binary number is as follows,

c.

Explanation of Solution

To compute “NOT(NOT(1101))”:

• First compute “NOT (1101)”,
  • The NOT operation can be applied on each bits individually and hence it is called bit-wise NOT operation.
  • The NOT operation for the binary number “1101” is as follows,

• The output bit is “0”, when the input bit is “1” and the output bit is “1”, when the input bit is “0”.
• The result of the above calculation is “0010”...

d.

Explanation of Solution

To compute “(0110 OR 0000) AND 1111”:

• First compute “(0110 OR 0000)”,
  • The OR operation can be applied on each pair of bits individually and hence it is called bit-wise OR operation.
  • The OR operation for the given binary number is as follows,

• The output bit is “1”, when one or both of the input bits are “1” and the output bit is “0”, when both the input bits are “0”.
• The result of the above calculation is “0110”.
• Compute “0110 AND 1111”,
• The AND operation can be applied on each pair of bits individually and hence it is called bit-wise AND operation...