Foundations of Higher Radix Numeric Computation

Radix arithmetic is based on radix polynomials with addition and multiplication being polynomial arithmetic. The distinguishing feature of radix polynomials is the carry operation which identifies congruent radix polynomials modulo (x - r) where the constant r is the radix. The carry operation can be employed to reduce the range of coefficients of polynomials over the integers to prescribed "digit sets" which may provide canonical representations or allow redundancy. We describe choices of digit sets for higher radices employed to allow more efficient hardware depending on properties of the circuitry, whether binary or multi-valued. We describe current applications of non standard digit sets in commodity microprocessors. We close with some observations on a discrete log representation of integers where the logarithmic base is a small prime.