enddigit

Enddigit is a term used to denote the units digit of an integer in a given base, most often base 10. In decimal notation, the enddigit of an integer n is the digit in the ones place, equivalently the value |n| mod 10. In modular arithmetic, enddigit refers to the residue of n modulo 10.

Computing the enddigit is straightforward: take the absolute value of the number and reduce modulo 10. Many programming languages implement this as enddigit = abs(n) % 10; some languages have different results for negative numbers due to their modulo convention, so using the absolute value is common. The enddigit is invariant under addition or subtraction of multiples of 10. The concept generalizes to other bases: the enddigit in base b is n mod b, yielding a value in 0..b−1.

Applications include quick arithmetic checks, pattern analysis of last digits of powers, and tasks where only the units digit is relevant. The last digit of the sum or product can be determined by the last digits of the addends or multipliers, respectively, using modular arithmetic.

Examples: enddigit(1234) = 4; enddigit(-987) = 7. The units digit of powers also follows a cycle depending on the base: for instance, the last digit of powers of 2 cycles through 2, 4, 8, 6.

Generalization and related concepts: in any base b, enddigit(n) = n mod b, with the result in 0 to b−1. See also units digit, last digit, and modular arithmetic.