Answer
The incorrect results due to overflow are in options c and f.
Work Step by Step
Let's go through each addition:
a. 00101 + 01000
Decimal: 00101 = 5, 01000 = 8
Sum: 5 + 8 = 13
Binary: 01101
13 is in range (-16 to 15)
No overflow
b. 11111 + 00001
Decimal: 11111 = -1, 00001 = 1
Sum: -1 + 1 = 0
Binary: 00000
No overflow
c. 01111 + 00001
Decimal: 01111 = 15, 00001 = 1
Sum: 15 + 1 = 16
Binary (6-bit needed) = 10000 → but in 5-bit two’s complement, 10000 = -16
Result is incorrect due to overflow
d. 10111 + 11010
Decimal: 10111 = -9, 11010 = -6
Sum: -9 + (-6) = -15
Binary: 10001
-15 is in range (-16 to 15)
No overflow
e. 11111 + 11111
Decimal: 11111 = -1, 11111 = -1
Sum: -1 + (-1) = -2
Binary: 11110
-2 is in range (-16 to 15)
No overflow
f. 00111 + 01100
Decimal: 00111 = 7, 01100 = 12
Sum: 7 + 12 = 19
Binary (needs more than 5 bits): 10011 → in 5-bit two’s complement = -13
Result is incorrect due to overflow
