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by omnicognate
760 days ago
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Grammar nazi correction, but one I think is both interesting and a useful way to remember how these work: ones' complement has the apostrophe at the end (but two's complement is correct). Ones' complement is the "complement of ones (plural)" in that if you take an n-bit number and the representation of its additive inverse in that scheme and add them as ordinary binary numbers you get a result that is n ones. Eg. using 4 bits, 6 is 0110, -6 is 1001, adding them with ordinary binary addition gives 1111. Two's complement is the "complement of two (to the n)" in that if you do the same thing you get 2^n. Eg. 6 is 0110, -6 is 1010, adding them with ordinary binary addition gives 10000, or 2^4. |
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“Some people, notably Donald Knuth, recommend using the placement of the apostrophe to distinguish between the radix complement and the diminished radix complement. In this usage, the four's complement refers to the radix complement of a number in base four while fours' complement is the diminished radix complement of a number in base 5. However, the distinction is not important when the radix is apparent (nearly always), and the subtle difference in apostrophe placement is not common practice. Most writers use one's and nine's complement, and many style manuals leave out the apostrophe, recommending ones and nines complement.”
I.e., the distinction isn’t as well established as some claim, and in the context of binary presentations it doesn’t really matter.