Complementary Two-Way Algorithms for Negative Radix Conversions

This paper describes two sets of algorithms in positive radix arithmetic for conversions between positive and negative integral radix representation of numbers. Each set consists of algorithms for conversions in either direction; these algorithms are mutually complementary in the sense they involve inverse operations depending upon the direction of conversion. The first set of algorithms for conversion of numbers from positive to negative radix (negative to positive radix) proceeds serially from the least significant end of the number and involves complementation and addition (subtraction) of unity on single-digit numbers. The second set of algorithms for conversion of numbers from positive to negative radix (negative to positive radix) proceeds in parallel starting from the full number (the most significant end of the number) and involves complementation and right (left) shift operations. The applications of these algorithms to integers, mixed integer-fractions, floating-point numbers, and for real-time conversions are given.