Eliminating the Normalization Problem in Digit

Richard J. Zaccone, Jesse L. Barlow

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In digit online arithmetic, operands are introduced a digit at a time. After the first few operand digits have been introduced, the result begins to appear a digit at a time. This feature of digit online arithmetic allows a significant amount of overlapping of arithmetic operations. Digit online arithmetic can sometimes produce unnormalized results. This can present a problem for the divide and square root algorithms. If the divisor and radicand are highly unnormalized, these algorithms will not produce the correct results. Two advances in overcoming this problem are presented. First, several techniques for producing results that are closer to being normalized are developed. Second, it is shown that normalized results are not necessary for divide and square root to work properly. Combining these results yields algorithms that will always give the correct results.

Original languageEnglish (US)
Pages (from-to)36-46
Number of pages11
JournalIEEE Transactions on Computers
Issue number1
StatePublished - Jan 1987

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics


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