
a.
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.

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.
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=>
Two’s complement of value B value is “11111110”.
Adding the values of A and converted B is,
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=>
Two’s complement of value B value is “00000010”.
Adding the values of converted A and B is,
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=>
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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Chapter 3 Solutions
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