Using 8bit 2s complement arithmetic add 21 to 23 Using 8bit

Using 8-bit 2s complement arithmetic add -21 to 23.

Using 8-bit 2s complement arithmetic add -21 to 23? 00000010 Overflow 01000000 00100000 none of the choices

Solution

two’s complement of -21 is
Step 1: 21₁₀=00010101
Step 2: Take the complement: 11101010
Step 3: Add 1: 1110 1010 + 1 = 11101011

the two’s complement of 23

Step 1: 23₁₀=00010111
Step 2: Take the complement: 11101000

substracting A-B means A+(-B)

Adding

11101011

11101000

-------------

111010011

Since this result has 9 bits, which is too large for the register chosen, the leftmost bit
is truncated, resulting in the binary representation of the positive (it starts with a 0) integer 11010011.

so overflow occured