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- Digital_sum_in_base_b 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.".
- Digital_sum_in_base_b wikiPageID "2315118".
- Digital_sum_in_base_b wikiPageRevisionID "344719520".
- Digital_sum_in_base_b hasPhotoCollection Digital_sum_in_base_b.
- Digital_sum_in_base_b subject Category:Integers.
- Digital_sum_in_base_b type Abstraction100002137.
- Digital_sum_in_base_b type DefiniteQuantity113576101.
- Digital_sum_in_base_b type Integer113728499.
- Digital_sum_in_base_b type Integers.
- Digital_sum_in_base_b type Measure100033615.
- Digital_sum_in_base_b type Number113582013.
- Digital_sum_in_base_b 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.".
- Digital_sum_in_base_b label "Digital sum in base b".
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- Digital_sum_in_base_b sameAs Q5276173.
- Digital_sum_in_base_b sameAs Q5276173.
- Digital_sum_in_base_b sameAs Digital_sum_in_base_b.
- Digital_sum_in_base_b wasDerivedFrom Digital_sum_in_base_b?oldid=344719520.
- Digital_sum_in_base_b isPrimaryTopicOf Digital_sum_in_base_b.