Arithmetic Algorithms for Error-Coded Operands

Abstract

A set of arithmetic algorithms is described for operands that are encoded in the ``AN'' error-detecting code with the low-cost check modulus A = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> - 1. The set includes addition additive inverse (complementation), multiplication, division, roundoff, and two auxiliary algorithms: ``multiply by 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> - 1,'' and ``divide by 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> - 1.'' The design of a serial radix-16 processor is presented in which these algorithms are implemented for the low-cost AN code with A = 15. This processor has been constructed for the Jet Propulsion Laboratory STAR computer. The adaptation of ``two's complement'' arithmetic for an inverse-residue code is also described.