14addition

14addition is the arithmetic operation of adding numbers expressed in base-14 notation. In base-14, digits run from 0 through 9 and then letters A, B, C, and D represent the values 10 through 13. The rules of 14addition mirror those of decimal addition, with carries produced whenever a digit sum reaches or exceeds 14.

Notation and rules: To add two numbers, align them by their least significant digits, add the corresponding digits with any carry from the previous step, and compute s = a_i + b_i + carry. If s is at least 14, set carry to 1 and the result digit to s − 14; otherwise carry is 0 and the result digit is s. Continue until all digits are processed; if a final carry remains, it is appended as the most significant digit.

Identity and properties: 14addition is commutative and associative, just like ordinary addition. The additive identity is 0, since 0 + x = x for any number x in base-14 notation.

Examples: 9 + 5 = 10 (base-14). 9D + 4 = 103 (base-14) because 9D equals 126 + 13 = 139 in decimal, plus 4 equals 143, which is 10·14 + 3. A + B equals 17 (base-14) since 10 + 11 = 21 decimal, which is 1·14 + 7. 7 + 9 = 12 (base-14).

Context and usage: Base-14 arithmetic is a specialization of positional numeral systems and is not widely used in everyday computation, but it can appear in theoretical discussions, numeral theory, or contexts where base-14 digits provide a convenient grouping or representation. See also base-n numeral systems.