Question

1. (20 pts) Perform the following operation:

   • (4−12)10,
   Using signed binary, 8–bit 2’s complement arithmetic.

Answer 1

(4-12)10 using 8bit 2's complement

4 in 8 bit binary
0000 0100

12 in 8 bit binary 0000 1100
1's complement of 12 => 1111 0011
2's complement of 12=> 11110011
+ 1
=11110100

-12 in binary is 11110100

4+(-12) =>

0000 0100
+1111 0100
= 1111 1000
as there is no carry we will take two's complement of this and the output will be negative

one's complement of 1111 1000 is 0000 0111
2's complement = 0000 0111
+ 1
=0000 1000
so the if we convert this into decimal it will be -8 which is the exact result of 4-12.

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