Problem 37E

How is the one's complement representation of the sum of two integers obtained from the one's complement representations of these integers?

Solution:

Step1

Given that

We have to find that how is the one's complement representation of the sum of two integers obtained from the one's complement representations of these integers?

Step2

The one’s complement of a binary number is characterized as the value obtained by inverting every one of the bits in the binary representation of the number.

An N-bit one’s complement numeral system can just represent whole numbers in the range

In one's complement addition of signed numbers is performed by using binary addition with end-around carry. If there is a carry-out of the most significant bit of the sum, this bit must be added to the least significant bit of the sum.

Step3

## For addition of decimal 17 to decimal -8 in 8-bit one's complement

17(0001 0001) and -8(1111 0111)

0001 0001

1111 0111

-----------------

1 0000 1000

From 1 0000 1000 1 is added again

0000 1000

1

--------------

0000 1001

0000 1001 represents 9.