Question

Write the results of the following additions as both eight-bit binary and

decimal numbers. For each part, use standard binary addition as
described in Section 2.5.1.
a. Add the 1’s complement representation of 7 to the 1’s complement
representation of −7.
b. Add the signed magnitude representation of 7 to the signed
magnitude representation of −7.
c. Add the 2’s complement representation of 7 to the 2’s complement
representation of −7.

Answer 1

The results are:

a. 1111 (1's complement representation)

b. 0010 (signed magnitude representation)

c. 0000 (2's complement representation)

Add the 1’s complement representation of 7 to the 1’s complement representation of -7.

1's complement representation of 7:

1's complement representation of -7 (flip all bits of 7):

1000

So, to add these two binary numbers:

0111 (+7 in 1's complement)

+1000 (-7 in 1's complement, flipped)

=

1111 (Discard the carry)