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# Division Method

IP.com Disclosure Number: IPCOM000095297D
Original Publication Date: 1965-Nov-01
Included in the Prior Art Database: 2005-Mar-07
Document File: 2 page(s) / 17K

IBM

## Related People

Miller, RE: AUTHOR [+2]

## Abstract

This division method uses signed-digit representation and carry-save addition to achieve a very high degree of parallelism and therefore, very rapid division. Several bits of initial quotients are formed simultaneously. The first initial quotient is estimated. It is then tested by multiplying it by the divisor and subtracting it from appropriate bits of the dividend. The subtraction is done starting with the most significant bits. When several bits of the remainder are formed, a new estimating operation can begin while the remainder of the subtraction operation is being performed.

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Division Method

This division method uses signed-digit representation and carry-save addition to achieve a very high degree of parallelism and therefore, very rapid division. Several bits of initial quotients are formed simultaneously. The first initial quotient is estimated. It is then tested by multiplying it by the divisor and subtracting it from appropriate bits of the dividend. The subtraction is done starting with the most significant bits. When several bits of the remainder are formed, a new estimating operation can begin while the remainder of the subtraction operation is being performed.

The estimating and testing operations proceed until all bits of the dividend are used. If any of the initial estimated quotients is too high, the next quotient estimated is a minus quantity. As estimating and testing operations proceed, initial quotients being formed are either added or subtracted, depending on their sign, from the sum of quotient bits previously formed. At the end of division, the desired quotient is stored as a result of the summing operation. The following is a detailed description of the division method.

Assume a quotient Q x 2/s//3/ = X x 2/s/1/Y x 2/s//2/ is formed where X, Y, and Q are n-bit positive integers. The division method forms the quotient Q. The exponent s/3/ is assumed to be formed separately. An initial quotient is formed g-bits at a time, starting with the most significant end. Later this initial quotient can require correction. It is...