Quiz Entry - updated: 2026.07.14
Why did computer architects choose two's complement over other signed number representations?
It lets one adder handle both signed and unsigned numbers, and it has a single zero — unlike sign-magnitude and one's complement.
Alternative representations considered:
| Method | -5 (4-bit) | Problem |
|---|---|---|
| Sign-magnitude | 1101 (1=neg, 101=5) | Need separate add/subtract circuits |
| One's complement | 1010 (flip all bits) | Two zeros (+0 and -0)! |
| Two's complement | 1011 | Addition just works ✓ |
Why two's complement wins — the same binary addition just works:
0101 (+5)
+ 1011 (-5)