I'm reading through a computer architecture book and came across the following:
Assume you have a 8-bit cell. So there are 256 possible integer values. Non-negatives run from 0 to 127. Assuming two's complement binary representation, what is the sum of 97 + 45?
Unsigned is clearly 142, you can do it as 97 + 45 in decimal, or:
0110 0001
0010 1101 ADD
--------------
1000 1110
But when you perform two's complement, you take that result (1000 1110) and determine that it is negative since the sign bit is 1. Then take the one's complement of it:
NOT 1000 1110 = 0111 0001
Then determine its two's complement:
0111 0001
0000 0001 ADD
--------------
0111 0010
This number is 114 but because our original number had a 1 in the sign bit, it's -114.
Question(s):
Why go through all the trouble of having the two's complement to find -114? Since 97 and 45, why not just find the sum of the two positive integers as an unsigned value which fits within the range of an 8-bit cell (1111 1111 being 255). Is it just because the question asks for the two's complement?
Is -114 equivalent to 142? I believe so if you take the two's complement number line, yo get 142-256 which is -114. From this, I dont understand why you would want to even use two's complement if you are summing two positive values!
A 1's complement just means flip all the bits, a 2's complement means negate the value. So 1's complement for 8-bit results effectively in 255 - x and 2's in 256 - x. You achieve the result of a 2's complement by doing a 1's complement and adding 1.
The 142 in 8-bit is equal to -114. Don't get too confused about it.