Eight-Bit Binary Addition Examples
Here are some examples of binary addition performed on eight-bit unsigned numbers. There's no deep trick here — just fill out each number to eight bits, and force the sum to fit as well. If it does not fit, this is considered an “overflow,” and will be accompanied by a one bit carried out of the 128's place, a “carryout.” With unsigned numbers, overflow and carryout always occur together, though this is not true for two's complement additions.
1011 + 10010 = 11101:
 1 0 0 0 0 1 0 1 1 + 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1
No overflow. Sum is correct.
1010110 + 110100 = 10001010:
 1 1 1 1 0 1 0 1 0 1 1 0 + 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0
No overflow. Sum is correct.
11001011 + 1011010 = 100100101:
 1 1 1 1 1 1 1 0 0 1 0 1 1 + 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 1
Overflow. The carry-out is discarded, and the sum is not correct
1010001 + 11001 = 1101010:
 1 1 0 1 0 1 0 0 0 1 + 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0
No overflow. Sum is correct.
110001 + 11100100 = 100010101:
 1 1 1 0 0 1 1 0 0 0 1 + 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1
Overflow. The carry-out is discarded, and the sum is not correct
10011011 + 1001010 = 11100101:
 1 1 1 1 0 0 1 1 0 1 1 + 0 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1
No overflow. Sum is correct.