Question

Write the 8-bit signed-magnitude, two's complement, and ones' complement representations for each decimal number: +25, + 120, + 82, -42, -111.

Answer 1

Answer:

Let's convert the decimals into signed 8-bit binary numbers.

As we need to find the 8-bit magnitude, so write the powers at each bit.

      Sign -bit 64 32 16 8 4 2 1

+25 - 0 0 0 1 1 0 0 1

+120- 0 1 1 1 1 0 0 0

+82 - 0 1 0 1 0 0 1       0

-42 - 1 0 1 0 1 0 1 0

-111 - 1 1 1 0 1 1 1 1

One’s Complements:  

+25 (00011001) – 11100110

+120(01111000) - 10000111

+82(01010010) - 10101101

-42(10101010) - 01010101

-111(11101111)- 00010000

Two’s Complements:  

+25 (00011001) – 11100110+1 = 11100111

+120(01111000) – 10000111+1 = 10001000

+82(01010010) – 10101101+1= 10101110

-42(10101010) – 01010101+1= 01010110

-111(11101111)- 00010000+1= 00010001

Explanation:

To find the 8-bit signed magnitude follow this process:

For +120

• put 0 at Sign-bit as there is plus sign before 120.

• Put 1 at the largest power of 2 near to 120 and less than 120, so put 1 at 64.

• Subtract 64 from 120, i.e. 120-64 = 56.

• Then put 1 at 32, as it is the nearest power of 2 of 56. Then 56-32=24.

• Then put 1 at 16 and 24-16 = 8.

• Now put 1 at 8. 8-8 = 0, so put 0 at all rest places.

To find one’s complement of a number 00011001, find 11111111 – 00011001 or put 0 in place each 1 and 1 in place of each 0., i.e., 11100110.

Now to find Two’s complement of a number, just do binary addition of the number with 1.