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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 wikiPageLength "1618".
- Digital_sum_in_base_b wikiPageOutDegree "19".
- Digital_sum_in_base_b wikiPageRevisionID "344719520".
- Digital_sum_in_base_b wikiPageWikiLink Abelian_group.
- Digital_sum_in_base_b wikiPageWikiLink Associative_property.
- Digital_sum_in_base_b wikiPageWikiLink Binary_number.
- Digital_sum_in_base_b wikiPageWikiLink Binary_operation.
- Digital_sum_in_base_b wikiPageWikiLink Category:Integers.
- Digital_sum_in_base_b wikiPageWikiLink Commutative_property.
- Digital_sum_in_base_b wikiPageWikiLink Countable_set.
- Digital_sum_in_base_b wikiPageWikiLink Decimal.
- Digital_sum_in_base_b wikiPageWikiLink Direct_sum.
- Digital_sum_in_base_b wikiPageWikiLink Exclusive_or.
- Digital_sum_in_base_b wikiPageWikiLink Group_isomorphism.
- Digital_sum_in_base_b wikiPageWikiLink Identity_element.
- Digital_sum_in_base_b wikiPageWikiLink Inverse_element.
- Digital_sum_in_base_b wikiPageWikiLink Modular_arithmetic.
- Digital_sum_in_base_b wikiPageWikiLink Natural_number.
- Digital_sum_in_base_b wikiPageWikiLink Nim.
- Digital_sum_in_base_b wikiPageWikiLink Numeral_system.
- Digital_sum_in_base_b wikiPageWikiLink Parity_bit.
- Digital_sum_in_base_b wikiPageWikiLinkText "digital sum in base b".
- Digital_sum_in_base_b wikiPageWikiLinkText "digital sum".
- Digital_sum_in_base_b wikiPageUsesTemplate Template:Unreferenced.
- Digital_sum_in_base_b subject Category:Integers.
- Digital_sum_in_base_b type Integer.
- 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".
- Digital_sum_in_base_b sameAs Q5276173.
- Digital_sum_in_base_b sameAs m.07362s.
- Digital_sum_in_base_b sameAs Q5276173.
- Digital_sum_in_base_b wasDerivedFrom Digital_sum_in_base_b?oldid=344719520.
- Digital_sum_in_base_b isPrimaryTopicOf Digital_sum_in_base_b.