Perform subtraction on the given unsigned binary numbers usi

Perform subtraction on the given unsigned binary numbers using the 2\'s complement of the subtrahend. Where the result should be negative, find its 2\'s complement and affix a minus sign. 100110 - 11010 111010 - 101110 Convert 11011.0112 to Decimal

Solution

a) 100110 - 11010

The numbers of bits in the subtrahend is 5 while that of minuend is 6.
We make the number of bits in the subtrahend equal to that of minuend by taking a `0’ in the sixth place of the subtrahend.

Therefore, subtrahend = 011010

2’s complement of the subtrahend is : 100110
Adding it to the minuend

1 00110 ~ Minuend
1 00110 ~ 2\'s Complement of subtrahend

=Carry over 1 0 01100
After dropping the carry over we get the result of subtraction to be 001100.

b) 111010 - 101110

Minuend = 111010
Subtrahend = 101110

2’s complement of the subtrahend is : 010010
Adding it to the minuend

1 11010 ~ Minuend
0 10010 ~ 2\'s Complement of subtrahend

= Carry over 1 0 01100
After dropping the carry over we get the result of subtraction to be 001100.

2) (11011.011)₂

2⁴ x 1 + 2³ x 1 + 2² x 0 + 2¹ x 1 + 2⁰ x 1 + 2^-1 x 0 + 2^-2 x 1 + 2^-3 x 1
= 16 + 8 + 0 + 2 + 1 + 0 + 0.25 + 0.125
= 27.375