senary

Senary is the base-6 numeral system, a positional numeral system that uses six digits: 0, 1, 2, 3, 4, and 5. Each place value represents a power of six, with the rightmost digit representing six to the power of zero, the next representing six to the power of one, and so on.

Numbers in senary are written by combining these digits in decreasing powers of six. For example, the decimal numbers 0–5 are written as 0–5 in senary; decimal 6 is written as 10_6; decimal 7 as 11_6; decimal 10 as 14_6; decimal 45 as 113_6; and decimal 100 as 244_6. Converting between senary and decimal involves repeatedly dividing or multiplying by six and keeping track of remainders.

Arithmetic in senary follows the same rules as in other bases, with carries occurring when a digit would reach six. For example, 5_6 + 3_6 equals 12_6 (since 5 + 3 = 8 in decimal, which is 1×6 + 2).

Senary is not widely used in everyday computing, where decimal and binary are predominant. It has niche uses in mathematics, education, and theoretical discussions about numeral systems, and it can be convenient for counting in groups of six or for certain combinatorial problems. Conversion between senary and decimal (or other bases) typically requires repeated division or multiplication by six.

The term senary also appears as an adjective meaning “of six.” In practice, senary remains primarily of academic interest and in contexts that explore base-6 representation.