ternaryquaternary

Ternaryquaternary is a term used to describe a mixed-radix numeral concept that combines ternary (base-3) and quaternary (base-4) representations in alternating positions or layers. In its simplest form, the system uses a sequence of bases 3, 4, 3, 4, and so on. The value of a digit sequence d0, d1, d2, d3, ... is computed as d0 + 3*d1 + 12*d2 + 36*d3 + ..., with d0 in 0–2, d1 in 0–3, d2 in 0–2, d3 in 0–3, and so forth. This yields 12 distinct two-digit values, 144 distinct four-digit values, etc.

Example: The digits (d3,d2,d1,d0) = (0,1,1,2) encode the value 0*36 + 1*12 + 1*3 + 2 = 17 in decimal.

Relationship to other systems: It is not a standard numeral base used widely; it is mainly of theoretical interest or used in discussions of mixed-radix arithmetic. It can be converted to and from decimal by applying the positional weights, and it can be extended to any length by continuing the alternating bases.

Applications and challenges: Potential applications include data encoding schemes that align with hardware or protocols that naturally separate 3- and 4-valued digits, educational demonstrations of mixed-radix arithmetic, and exploratory research in numeral systems. However, a lack of conventional hardware support and the complexity of arithmetic operations limit practical adoption.

See also: Mixed radix numeral system, ternary numeral system, quaternary numeral system.