Arithmetic Algorithms for Error-Coded Operands

  • Authors:
  • Algirdas Avizienis

  • Affiliations:
  • Department of Computer Science, University of California, Los Angeles, Calif. 90024, and the Jet Propulsion Laboratory, Pasadena, Calif. 91103.

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 1973

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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 = 2a - 1. The set includes addition additive inverse (complementation), multiplication, division, roundoff, and two auxiliary algorithms: ``multiply by 2a - 1,'' and ``divide by 2a - 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.