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Division Using Addition

IP.com Disclosure Number: IPCOM000094070D
Original Publication Date: 1966-May-01
Included in the Prior Art Database: 2005-Mar-06
Document File: 2 page(s) / 14K

Publishing Venue

IBM

Related People

Brady, JA: AUTHOR

Abstract

Division of any number by a preselected divisor DR is accomplished by adding the position related quotients PRQ's for the coded ordinal positions associated with the number being divided. The PRQ's are obtained by dividing any one only of the ordinal values of the numbering system by the preselected DR. This PRQ is then stored and employed in a shifted or otherwise modified form as required to effect the entire division of any number.

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Division Using Addition

Division of any number by a preselected divisor DR is accomplished by adding the position related quotients PRQ's for the coded ordinal positions associated with the number being divided. The PRQ's are obtained by dividing any one only of the ordinal values of the numbering system by the preselected DR. This PRQ is then stored and employed in a shifted or otherwise modified form as required to effect the entire division of any number.

As an example, it is assumed that the preselected DR is 1.024. To obtain the related quotient Q, this number is divided into any one value of an ordinal of the numbering system being used. In the natural binary system the ordinal values are defined by the series In.... 64, 32, 8, 4, 2, 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64... 1/n.

The PRQ for ordinal value 16 is obtained by dividing 16 by the preselected number 1.024. The PRQ is 15.625 which is expressed in the natural binary form as follows:
Ordinal value 32 16 8 4 2 1 1/2 1/4 1/8 1/16
15.625 0 0 1 1 1 1 1 0 1 0

X.

An indicator or tag X is associated with this binary number to indicate that with different ordinal values the number should be formed around that position. Thus, the above is correct for 16, and the same series of 1's and 0's is used for any other ordinal. For example, the two-valued ordinal is represented by the same series, but with the first binary 1 one in the Q sequence being in the ordinal immediately to the right of the two-valued ordinal, i.e., the one-valued ordinal. PRQ's are computed in a similar manner for each DR which is to be used in other division operations. All resulting PRQ's are stored where they are quickly accessible, such as in a magnetic core storage unit.

If it is desired to divide any number by the preselected DR, it is only necessary to add the PRQ's for the number being divided to obtain the answer. The addition should be kept in accordance with the significance of each ordinal of the dividend DD, and no addition of the corresponding Q should be made for any ordinal the significance of which is 0.

As an example, to divide 5281 by 1.024, it is determined that this number appears in binary form as follows: Ordinal value 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1 5281 0 1 0 1 0 0 1 0 1 0 0 0 0 1 Division by additio...