• 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.
|
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.
![[^]](http://sandbox.mc.edu/icons/local//up3.gif){kind=icon}