Question

Convert each of the following 8-bit 2's-complement numbers to decimal form. (16 points) a) 01001000 b) 01010101 c) 10101010

Answer 1

Answer:

a) 72

b) 85

c) -86

Explanation:

A 2's-complement numbers is converted to decimal form by multiplying each instance of 1 by 2^(position -1) and adding the sub-results.

a) 01001000 =>

1* 2^(7-1) + 1*2^(4-1) = 64+8 = 72

b) 01010101 =>

1* 2^(7-1) + 1*2^(5-1) + 1*2^(3-1) + 1*2^(1-1) = 64+16+4+1 = 85

c) 10101010

1's complement of the given number by bit inversion is 01010101

2's complement is obtained by adding 1 to the 1's complement.

=01010110

In decimal this is : 1*2^(7-1)+1*2^(5-1)+1*2^(3-1)+1*2^(2-1) = 64+16+4+2 = 86

So the original number is negative of this = -86

Answer 2

Answer:hsgshh

Explanation: