A Generalized Multibit Recoding of Two's Complement Binary Numbers and its Proof with Application in Multiplier Implementations

  • Authors:
  • H. Sam;A. Gupta

  • Affiliations:
  • -;-

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 1990

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Abstract

A multibit recoding algorithm for signed two's complement binary numbers is presented and proved. In general, a k+1-bit recoding will result in a signed-digit (SD) representation of the binary number in radix 2/sup k/, using digits -2/sup k-1/ to +2/sup k-1/ including 0. It is shown that a correct SD representation of the original number is obtained by scanning K+1-tuples (k驴1) with one bit overlapping between adjacent groups. Recording of binary numbers has been used in computer arithmetic with 3-bit recoding being the dominant scheme. With the emergence of very high speed adders, hardware parallel multipliers using multibit recoding with k