Computer Science Illuminated
Computer Science Illuminated
6th Edition
ISBN: 9781284055917
Author: Nell Dale, John Lewis
Publisher: Jones & Bartlett Learning
Question
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Chapter 3, Problem 40E

a.

Program Plan Intro

Given information:

  • The value of A is given as 11111110.
  • The value of B is given as 00000010.

Two’s complement:

  • Change the entire bit “0” to bit“1” and all the bit “1” to bit “0”.
  • Add the Value “1” to the above converted binary string.
  • It results into two’s complement of a given binary number.

a.

Expert Solution
Check Mark

Explanation of Solution

Calculating value for an expression “A+B” using two’s complement:

To evaluate the result of the given expression “A+B”, substitute the value of A as “11111110” and B as “00000010” in the expression.

A+B=>

In this expression two’s complement is not needed since A and B is non-negative values.

11111110+00000010_00000000

Therefore, the calculated value of given expression “A+B” is “00000000”.

Explanation of Solution

b.

Calculating value for an expression “A-B” using two’s complement:

To evaluate the result of the given expression “A-B”, substitute the value of A as “11111110” and B as “00000010” in the given expression.

A-B=>

In this expression two’s complement is needed for B since it contains negative value.

To calculate two’s complement of value B=>

0000001011111101+1_11111110

Two’s complement of value B value is “11111110”.

 Adding the values of A and converted B is,

11111110+11111110_11111100

Overflow bit has occurred in the above calculation. This extra bit is ignored to assign the result in its allocated bits.

Therefore, the calculated value of given expression “A-B” is “11111100”.

Explanation of Solution

c.

Calculating value for an expression “B-A” using two’s complement:

To evaluate the result of the given expression “B-A”, substitute the value of A as “11111110” and B as “00000010” in the given expression.

B-A=>

In this expression two’s complement is needed for A since it contains negative value.

To calculate two’s complement of value A=>

1111111000000001+1_00000010

Two’s complement of value B value is “00000010”.

Adding the values of converted A and B is,

00000010+00000010_00000100

Therefore, the calculated value of given expression “B-A” is “00000100”.

Explanation of Solution

d.

Calculating value for an expression “-B” using two’s complement:

To evaluate the result of the given expression “-B”, substitute the value of B as “00000010” in the given expression.

-B=>

In this expression two’s complement is needed for B since it contains negative value.

To calculate two’s complement of value B=>

0000001011111101+1_11111110

Two’s complement of value B value is “11111110”.

Therefore, the calculated value of given expression “-B” is “11111110”.

Explanation of Solution

e.

Calculating value for an expression “-(-A)” using two’s complement:

The given expression can be written as,

-(-A)=+A

Two’s complement is not needed for the value “A” since it contains positive value.

Therefore, the calculated value of given expression “-(-A)” is same as the given value “11111110”.

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