A New Binary Number Code and a Multiplier, Based on 3 as Semi-Primitive Root of 1 Mod 2

The group of units mod (prime p>2) is known to be cyclic for k ≥ 1. For k=1 this corresponds to Fermat's Small Theorem: n= 1 mod p (n coprime to p). If p=2 and k > 2 the 2 units (odd residues) require two generators, such as 3 and -1 mod 2, since 3 is semi-primitive root of 1 mod 2. So each residue n = ± 3.2 mod 2 with unique non-negative i < 2, j ≤ k. For engineering purposes this yields efficient log-arithmetic with dual base 2 and 3