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SESK: Stuff Everyone Should Know · sesk.info/tech-twos-complement

How do nearly all computers store negative whole numbers in binary?

Two's complement: flip every bit, then add 1.

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  1. A sign bit plus the size
  2. Two's complement ✔
  3. One's complement

Why: Two's complement has only one zero, and the same adder circuit handles both addition and subtraction. Just using a sign bit wastes a pattern on minus zero. So two's complement became the standard.

Huh, didn't know that: Two's complement lets the same hardware perform signed and unsigned addition and subtraction.

The dad joke
Why was the negative number so nice? It always paid two's complements.
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References

Answer: Two's complement. Two's complement has only one zero, and the same adder circuit handles both addition and subtraction. Just using a sign bit wastes a pattern on minus zero. So two's complement became the standard.

  1. OpenStax Introduction to Computer Science 5.3: Machine-Level Information Representation openstax.org/books/introduction-computer-science/pages/5-3-machine-level-information-representation
    Therefore, a two's complement presentation of a signed number is the standard presentation in all computer system s.
    Checked 2026-10-10.

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