Complex Divider Eliminates Multipliers Using Adders and Bit Shifters

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Solution Overview

Problem

Conventional complex dividers require six real multipliers and two real dividers, increasing design complexity due to the need for complex number division operations.

Innovation Solution

A complex divider design that eliminates the use of multipliers by employing a computing unit to generate a third complex value and a real number, which are then used by a dividing unit to obtain the division result, utilizing only adders and bit shifters to adjust phases and perform division.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Device complexity

If conventional complex divider design is used with six real multipliers and two real dividers, then division accuracy is maintained, but device complexity increases

Engineering Contradiction:

Improvedivider structure complexityVSAvoiddivision accuracy

Core Design Contradiction:

Device complexityVSMeasurement precision

Solution Approach 1:

The patent changes the computational parameters by eliminating multipliers and using only adders, subtractors, and bit shift operations. This transforms the computational approach from multiplication-based to addition-based arithmetic, significantly reducing hardware complexity while maintaining division functionality through alternative mathematical formulations

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent extracts and removes the multiplier components from the complex divider structure. By taking out the six real multipliers and two real dividers from the conventional design, the invention simplifies the hardware architecture while preserving the essential division function through a different computational pathway using only additive operations

Inventive Principle:

Principle #2Taking out (Extraction)

2Ease of manufacture

If six real multipliers and two real dividers are used in complex division, then division function is achieved, but manufacturing complexity increases

Engineering Contradiction:

Improvedivider implementation easeVSAvoidmultiplier and divider circuit complexity

Core Design Contradiction:

Ease of manufactureVSDevice complexity

Solution Approach 1:

The patent replaces expensive and complex multiplier circuits with simpler, cheaper adder and bit-shifter circuits. This substitution uses less complex, more easily manufactured components that can be implemented with fewer transistors and simpler logic gates, making the divider easier to manufacture

Inventive Principle:

Principle #27Cheap short-living objects (Disposable)

Solution Approach 2:

The patent substitutes the mechanical/multiplicative operation system with an additive operation system. By replacing multipliers (complex mechanical-equivalent circuits) with adders and bit shifters (simpler digital logic), the invention achieves the same mathematical function through a different operational mechanism that is easier to implement in hardware

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Data Source

PatentUS8938486B2Complex divider and associated method

Publication Date: 2015.01.20 REALTEK SEMICON CORP

AI summary

A complex divider utilized for dividing a first complex number by a second complex number to generate a computing result includes a computing unit and a dividing unit. The computing unit is utilized for receiving the first complex value and the second complex value, generating a third complex value according to the first complex value and the second complex value, and generating a real number according to the second complex value. The dividing unit is coupled to the computing unit, and is utilized for receiving the third complex value and the real number and dividing the third complex value by the real number to obtain the computing result.