Division (mathematics)

About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.

Efficient initial approximation and fast converging methods for division and square root

Abstract: Efficient initial approximations and fast converging algorithms are important to achieve the desired precision faster at lower hardware cost in multiplicative division and square root. In this paper, a new initial approximation method for division, an accelerated higher order converging division algorithm, and a new square root algorithm are proposed. They are all suitable for implementation on an arithmetic unit where one multiply-accumulate operation, can be executed in one cycle. In the case of division, the combination of our initial approximation method and our converging algorithm, enables a single iteration of the converging algorithm to produce double-precision quotients. Our new square root algorithm can form, double-precision square roots faster using smaller look-up tables than the Newton-Raphson method. >

A Distribution Procedure for the Analysis of Slabs Continuous over Flexible Beams

Abstract: A report of an investigation conducted by the Engineering Experiment Station, University of Illinois in cooperation with the U.S. Bureau of Public Roads and the Illinois Division of Highways.

The CORDIC Computing Technique

Abstract: The "Coordinate Rotation DIgital Computer" computing technique can be used to solve, in one computing operation and with equal speed, the relationships involved in plane coordinate rotation; conversion from rectangular to polar coordinates; multiplication; division; or the conversion between a binary - and a mixed-radix system.

On Range-Transformation Techniques for Division

Abstract: This note points out the close relationship between some of the recently described division techniques, in which the divisor is transformed to a range close to unity. A brief theoretical analysis is presented which examines the choice of quotient digit when this type of division technique is used for conventional and signed-digit number systems.

Data processing system

Abstract: A data processing system having an arithmetic unit is designed for a multiplication of n-place numbers in 2's complement according to the Booth algorithm, and for division of unsigned numerals. A 2n-stage shift register is connected over a logical control circuit to the operation code inputs of an ALU. The control circuit automatically forms instruction code signals to the ALU as a function of informational bits derived from the shift register, whereas other operation code input signals are directly connected to the operation code inputs. The control circuit is a sequential circuit having a multiplexer for the selective through-connection of the multiplication code signals, the division code signals, or other operation code signals to the operation code inputs of the ALU.