5 ms·

A consequence of most, if not all, CPUs today using two's complement integers. I think one's complement is more sensible since it doesn't have this problem, bu

A consequence of most, if not all, CPUs today using two's complement integers. I think one's complement is more sensible since it doesn't have this problem, but it loses out because it requires a more complex ISA and implementation.

veltas 4y ago
It's annoying that negation, ABS, and division can overflow with two's complement. But how I look at it: lots of operations can already overflow, just a fact of signed integers, and you need to guard against that overflow in portable code already. It doesn't seem to be fundamentally worse that those extra operations can overflow.
deleted 4y ago
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nayuki 4y ago
Ones' complement (correct spelling) has negative zero, which I would argue is a far worse problem.
- xigoi 4y ago
  Why in the fuck is it “ones' complement”, but “two's complement”?
  - tsimionescu 4y ago
    According to Wikipedia: > The name "ones' complement" (note this is possessive of the plural "ones", not of a singular "one") refers to the fact that such an inverted value, if added to the original, would always produce an 'all ones' number
    - xigoi 4y ago
      And two's complement refers to what?
      - tsimionescu 4y ago
        The radix complement in base two. They are closely related but not identical - the two's complement representation of a negative number is the ones' complement representation + 1 (ignoring the final carry). In ones' complment there are two representations for 0 (all 0s or all 1s), but every number has a positive and negative representation. In two's complement, there is a single 0, but there is also negative number that doesn't have a corresponding positive representation (INT_MIN). In fact, for every numerical base there is an equivalent. For example, in base 3 you can represent a number in twos' complement notation (each trit X is replaced with 2-X, so -3 is represented as 212 on three trits, with +3 being 010) is or in three's complement by adding 1 (212+1 = 220). For base 10, you can do nines' complement (-3 on 3 digits is 996) or ten's complement (996+1 = 997).

veltas 4y ago

It's annoying that negation, ABS, and division can overflow with two's complement. But how I look at it: lots of operations can already overflow, just a fact of signed integers, and you need to guard against that overflow in portable code already. It doesn't seem to be fundamentally worse that those extra operations can overflow.

deleted 4y ago

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nayuki 4y ago

Ones' complement (correct spelling) has negative zero, which I would argue is a far worse problem.

xigoi 4y ago
Why in the fuck is it “ones' complement”, but “two's complement”?
- tsimionescu 4y ago
  According to Wikipedia: > The name "ones' complement" (note this is possessive of the plural "ones", not of a singular "one") refers to the fact that such an inverted value, if added to the original, would always produce an 'all ones' number
  - xigoi 4y ago
    And two's complement refers to what?
    - tsimionescu 4y ago
      The radix complement in base two. They are closely related but not identical - the two's complement representation of a negative number is the ones' complement representation + 1 (ignoring the final carry). In ones' complment there are two representations for 0 (all 0s or all 1s), but every number has a positive and negative representation. In two's complement, there is a single 0, but there is also negative number that doesn't have a corresponding positive representation (INT_MIN). In fact, for every numerical base there is an equivalent. For example, in base 3 you can represent a number in twos' complement notation (each trit X is replaced with 2-X, so -3 is represented as 212 on three trits, with +3 being 010) is or in three's complement by adding 1 (212+1 = 220). For base 10, you can do nines' complement (-3 on 3 digits is 996) or ten's complement (996+1 = 997).