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

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

+25-00011001

+120-01111000

+82-0101001       0

-42-10101010

-111-11101111

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

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.