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. Jump to: navigation, search Natural number can mean either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). Natural numbers have two main purposes: they can be used for counting (there are 3 apples on the table), and they can be used... Jump to: navigation, search A numeral is a symbol or group of symbols that represents a number. ...

For example in decimal (base 10) arithmetic, the digital sum of 123 and 789 is 802: Decimal, or less commonly, denary, usually refers to the base 10 numeral system. ...

• 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.

 123 789 --- 802 

More 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. Jump to: navigation, search The binary numeral system represents numeric values using two symbols, typically 0 and 1. ... Jump to: navigation, search Look up Parity on Wiktionary, the free dictionary Parity is a concept of equality of status or functional equivalence. ... Exclusive disjunction (usual symbol xor) is a logical operator that results in true if one of the operands (not both) is true. ...

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. Jump to: navigation, search Nim is a two-player mathematical game of strategy in which players take turns removing objects from heaps, one or more objects at a time but only from a single heap. ...

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. In mathematics, associativity is a property that a binary operation can have. ... In mathematics, especially abstract algebra, a binary operation * on a set S is commutative if x * y = y * x for all x and y in S. Otherwise * is noncommutative. ... In mathematics, a binary operation, or binary operator, is a calculation involving two input quantities and one kind of a specific operation. ... Jump to: navigation, search Natural number can mean either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). Natural numbers have two main purposes: they can be used for counting (there are 3 apples on the table), and they can be used... In mathematics, an identity element (or neutral element) is a special type of element of a set with respect to a binary operation on that set. ... In mathematics, the inverse of an element x, with respect to an operation *, is an element x such that their compose gives a neutral element. ... In mathematics, an abelian group, also called a commutative group, is a group (G, *) such that a * b = b * a for all a and b in G. Abelian groups are named after Niels Henrik Abel. ... Jump to: navigation, search In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations. ... In abstract algebra, the direct sum is a construction which combines several vector spaces (or groups, or abelian groups, or modules) into a new, bigger one. ... In mathematics the term countable set is used to describe the size of a set, e. ... Jump to: navigation, search Modular arithmetic is a system of arithmetic for integers, where numbers wrap around after they reach a certain value — the modulus. ...