Browse Prior Art Database

Base 10 Division of Binary Numbers

IP.com Disclosure Number: IPCOM000043704D
Original Publication Date: 1984-Sep-01
Included in the Prior Art Database: 2005-Feb-05

Publishing Venue

IBM

Related People

Authors:
Bellamy, LR [+details]

Abstract

Division by 10 can be reduced to shift and add instructions with the precision determined by the number of terms of a binary series expansion. Let x = binary number stored in M-processor register. (Image Omitted) The terms of the above series are all powers of two and can be computed quite rapidly by merely shifting x to the right a number of times equal to the exponent of the power of two. The error occurring due to this series approximation is independent of x and is strictly a function of the number of terms in the expansion; therefore, the user can specify in advance the accuracy desired and choose the number of terms accordingly. The error term is given by: (Image Omitted) For example, for n=3 (terms): (Image Omitted) For just four terms in the expansion, the error in the approximation is: (Image Omitted)