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# 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
Document File: 2 page(s) / 17K

IBM

## Related People

Bellamy, LR: AUTHOR

## 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)

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Base 10 Division of Binary Numbers

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)

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