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 - 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.