Respuesta :
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.
