Integer Divider Module Using Reciprocal Multiplication

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Solution Overview

Problem

Conventional digital circuits face inefficiencies in performing integer division operations, particularly when dealing with divisors that are sums of powers of two, leading to high computational complexity and power consumption.

Innovation Solution

The method involves expressing the divisor as 2n(1+2p), calculating the reciprocal of 1+2p as a binary fraction with alternating runs of binary '1's and '0's, and multiplying the dividend by this reciprocal before dividing by 2n to produce the division result, which can be implemented using simple hardware with recursive calculations.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Device complexity

If conventional long binary division is used, then division operations can be performed, but computational complexity and power consumption are high

Engineering Contradiction:

Improvecomputational complexityVSAvoiddivision operation efficiency

Core Design Contradiction:

Device complexityVSProductivity

Solution Approach 1:

The patent transforms the division operation into a multiplication operation by using the reciprocal of the divisor. Instead of performing complex division, the system calculates the reciprocal of the divisor (1/divisor) and multiplies it by the dividend. This parameter transformation from division to multiplication significantly reduces computational complexity and power consumption while maintaining accuracy.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces the mechanical division process with a multiplication process using reciprocal values. By substituting the division operation with multiplication by the reciprocal, the system achieves the same mathematical result with simpler hardware requirements and lower computational overhead, effectively replacing a complex mechanical operation with a simpler equivalent.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Reliability

If conventional division circuits are used, then division can be performed, but power consumption is high

Engineering Contradiction:

Improvedivision operation accuracyVSAvoidpower consumption

Core Design Contradiction:

ReliabilityVSUse of energy by moving object

Solution Approach 1:

The patent changes the operational parameter from division to multiplication by using the reciprocal of the divisor. This parameter change allows the system to achieve the same computational result with significantly lower power consumption, as multiplication circuits consume less power than division circuits while maintaining the same level of accuracy.

Inventive Principle:

Principle #35Parameter changes

3Adaptability or versatility

If standard division algorithms are used, then general division is supported, but computation time is linear with dividend size

Engineering Contradiction:

Improvedivision algorithm applicabilityVSAvoidcomputation time

Core Design Contradiction:

Adaptability or versatilityVSLoss of time

Solution Approach 1:

The patent transforms the division algorithm into a multiplication algorithm using reciprocals. This parameter transformation changes the time complexity from linear O(n) to a more efficient computation that requires fewer operational steps, thereby reducing computation time while maintaining broad applicability to different dividend and divisor values.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS9032010B2Integer divider module

Publication Date: 2015.05.12 MELLANOX TECHNOLOGIES LTD(IL)

AI summary

A method includes receiving a dividend and a divisor for performing a division operation. Numbers p and n are found, for which the divisor equals 2n(1+2p). An interim result, which is equal to a reciprocal of 1+2p multiplied by the dividend, is calculated. The interim result is divided by 2n to produce a result of the division operation.