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# Determination of Remainder in Normal Clocking Cycle

IP.com Disclosure Number: IPCOM000093946D
Original Publication Date: 1966-Apr-01
Included in the Prior Art Database: 2005-Mar-06
Document File: 2 page(s) / 77K

IBM

## Related People

Hornung, LM: AUTHOR

## Abstract

The drawing shows a logic arrangement for operating upon the bits of the three lowest ordinals of both a natural binary quotient and dividend. For these three bits the logic implements the formula Dividend Quotient-4 X Quotient, where the quotient is the whole number quotient from a division by 5. The output represents the remainder from a division by 5, and can be used immediately in the technique for radix conversion based upon a division by 10 to convert a natural binary number to a decimal number.

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Determination of Remainder in Normal Clocking Cycle

The drawing shows a logic arrangement for operating upon the bits of the three lowest ordinals of both a natural binary quotient and dividend. For these three bits the logic implements the formula Dividend Quotient-4 X Quotient, where the quotient is the whole number quotient from a division by 5. The output represents the remainder from a division by 5, and can be used immediately in the technique for radix conversion based upon a division by 10 to convert a natural binary number to a decimal number.

A primary value of this arrangement is realized because it avoids the existence of a typical machine clocking to continue a division into the fractional ordinals of a number. Instead, a dividend is divided from its highest order. This occurs until the quotient ordinal is produced which corresponds to the lowest ordinal of the dividend being operated upon. Then the remainder is determined by the circuit shown.

The circuit is an implementation of the formula: Remainder (Div. by 5) = Dividend - 5 X Quotient (Div. by 5), which can be arranged to read R(5) = D - Q(5) - 4Q(5). Since a remainder from a division by 5 cannot be greater than 4, it is realized that only the three lowest ordinals of D, Q, and R need not be considered. The above logic is based directly on the basic equation considering only those three lowest ordinals. An advantage of the logic shown is that it is only a slight addition and modification to para...