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- Q5276173 subject Q7028429.
- Q5276173 abstract "The digital sum in base b of a set of natural numbers is calculated as follows: express each of the numbers in base b, then take the sum of corresponding digits and discard all carry overs. That is, the digital sum is the same as the normal sum except that no carrying is used.For example in decimal (base 10) arithmetic, the digital sum of 123 and 789 is 802:3 + 9 = 12, discard the 10 leaving 2.2 + 8 = 10, discard the 10 leaving 0.1 + 7 = 8, there is no carry to discard.123789---802More usually the digital sum is calculated in binary (base 2) where the result only depends upon whether there are an even or odd number of 1s in each column. This is the same function as parity or multiple exclusive ors.For example:011 (3)100 (4)101 (5)---010 (2) is the binary digital sum of 3, 4 and 5.The binary digital sum is crucial for the theory of the game of nim.The digital sum in base b is an associative and commutative operation on the natural numbers; it has 0 as neutral element and every natural number has an inverse element under this operation. The natural numbers together with the base-b digital sum thus form an abelian group; this group is isomorphic to the direct sum of a countable number of copies of Z/bZ.".
- Q5276173 wikiPageWikiLink Q122653.
- Q5276173 wikiPageWikiLink Q13582243.
- Q5276173 wikiPageWikiLink Q164307.
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- Q5276173 wikiPageWikiLink Q185813.
- Q5276173 wikiPageWikiLink Q21199.
- Q5276173 wikiPageWikiLink Q319400.
- Q5276173 wikiPageWikiLink Q338057.
- Q5276173 wikiPageWikiLink Q3913.
- Q5276173 wikiPageWikiLink Q498186.
- Q5276173 wikiPageWikiLink Q625502.
- Q5276173 wikiPageWikiLink Q7028429.
- Q5276173 wikiPageWikiLink Q724409.
- Q5276173 wikiPageWikiLink Q742064.
- Q5276173 wikiPageWikiLink Q81365.
- Q5276173 comment "The digital sum in base b of a set of natural numbers is calculated as follows: express each of the numbers in base b, then take the sum of corresponding digits and discard all carry overs.".
- Q5276173 label "Digital sum in base b".