2024-03-19 07:20:03 +00:00
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---
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id: gktb
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title: Two's complement
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tags: []
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created: Tuesday, March 19, 2024
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---
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# Two's complement
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## Summary
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- _Two's complement_ is a method for representing signed numbers (negative
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integers) in binary.
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2024-03-19 07:30:04 +00:00
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- The two's complement of a given binary integer is its negative equivalent.
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2024-03-19 07:20:03 +00:00
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## Detail
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2024-03-19 07:30:04 +00:00
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### Procedural steps
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Two's complement divides the available word length (see
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[[Binary_encoding|binary encoding]]) into two subsets: one for negative integrs
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and one for positive integers.
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Take the binary encoding of decimal five (`0101`). Its complement is `1011`.
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The procedure for deriving the complement is as follows.
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To derive the complement of an unsigned number:
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1. Take the unsigned number and invert its digits: `0` becomes `1`, `1` becomes
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`0`
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2. Add one
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To derive the unsigned equivalent of a signed number
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### Formal expression
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2024-03-19 07:20:03 +00:00
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## Applications
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## Related notes
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[[Signed_and_unsigned_numbers|signed_and_unsigned_numbers]]
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