An efficient algorithmic framework to minimize the summand matrix in binary multiplication

Binary multiplication is a key operation in digital systems, often limited by the complexity of generating and summing numerous partial products. Traditional methods, like Booth’s algorithm, produce a summand matrix proportional to the operand bit-length, increasing computational load, hardware usag...

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Main Authors: Amit Verma, Manish Prateek, Shiv Naresh Shivhare, Thipendra P. Singh, Anuj Kumar, Rakesh Ranjan, Rahul Priyadarshi
Format: Article
Language:English
Published: Taylor & Francis Group 2025-10-01
Series:Automatika
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Online Access:https://www.tandfonline.com/doi/10.1080/00051144.2025.2526261
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author Amit Verma
Manish Prateek
Shiv Naresh Shivhare
Thipendra P. Singh
Anuj Kumar
Rakesh Ranjan
Rahul Priyadarshi
author_facet Amit Verma
Manish Prateek
Shiv Naresh Shivhare
Thipendra P. Singh
Anuj Kumar
Rakesh Ranjan
Rahul Priyadarshi
author_sort Amit Verma
collection DOAJ
description Binary multiplication is a key operation in digital systems, often limited by the complexity of generating and summing numerous partial products. Traditional methods, like Booth’s algorithm, produce a summand matrix proportional to the operand bit-length, increasing computational load, hardware usage and latency. To address these issues, we propose a novel binary multiplication algorithm that minimizes the number of required summands. By selectively using the smaller operand and employing targeted shift operations, our method avoids recursive bit-level multiplications and reduces summands to as few as 1–5 for odd and 1–4 for even operands. This approach achieves a lower time complexity of O(log2n), offering significant speed improvements over existing algorithms. Moreover, it leads to a reduction in hardware components by approximately 40–75%, contributing to notable power savings. The algorithm is fully compatible with existing parallel adder circuits, ensuring ease of integration. Its simplicity and efficiency make it ideal for low-power arithmetic units, embedded systems and DSP applications. Future work will focus on supporting signed multiplications and integrating the algorithm into VLSI designs for real-world applications, enhancing its appeal in resource-constrained computing environments.
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issn 0005-1144
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spelling doaj-art-76f9d2f387664e7999568925793ee7082025-08-20T03:50:07ZengTaylor & Francis GroupAutomatika0005-11441848-33802025-10-01664223110.1080/00051144.2025.2526261An efficient algorithmic framework to minimize the summand matrix in binary multiplicationAmit Verma0Manish Prateek1Shiv Naresh Shivhare2Thipendra P. Singh3Anuj Kumar4Rakesh Ranjan5Rahul Priyadarshi6School of Computer Science, UPES, Dehradun, IndiaComputer Science and Engineering, DBS Global University, Dehradun, IndiaSchool of Computer Science Engineering and Technology, Bennett University, Greater Noida, IndiaSchool of Computer Science Engineering and Technology, Bennett University, Greater Noida, IndiaDepartment of Computer Science, Doon University, Dehradun, IndiaSchool of Computer Science, UPES, Dehradun, IndiaFaculty of Engineering and Technology, ITER, Siksha ‘O’ Anusandhan (Deemed to Be University), Bhubaneswar, Odisha, IndiaBinary multiplication is a key operation in digital systems, often limited by the complexity of generating and summing numerous partial products. Traditional methods, like Booth’s algorithm, produce a summand matrix proportional to the operand bit-length, increasing computational load, hardware usage and latency. To address these issues, we propose a novel binary multiplication algorithm that minimizes the number of required summands. By selectively using the smaller operand and employing targeted shift operations, our method avoids recursive bit-level multiplications and reduces summands to as few as 1–5 for odd and 1–4 for even operands. This approach achieves a lower time complexity of O(log2n), offering significant speed improvements over existing algorithms. Moreover, it leads to a reduction in hardware components by approximately 40–75%, contributing to notable power savings. The algorithm is fully compatible with existing parallel adder circuits, ensuring ease of integration. Its simplicity and efficiency make it ideal for low-power arithmetic units, embedded systems and DSP applications. Future work will focus on supporting signed multiplications and integrating the algorithm into VLSI designs for real-world applications, enhancing its appeal in resource-constrained computing environments.https://www.tandfonline.com/doi/10.1080/00051144.2025.2526261Binary multiplicationlatency optimizationmultipliersummand reductionBooth’s algorithmhardware efficiency
spellingShingle Amit Verma
Manish Prateek
Shiv Naresh Shivhare
Thipendra P. Singh
Anuj Kumar
Rakesh Ranjan
Rahul Priyadarshi
An efficient algorithmic framework to minimize the summand matrix in binary multiplication
Automatika
Binary multiplication
latency optimization
multiplier
summand reduction
Booth’s algorithm
hardware efficiency
title An efficient algorithmic framework to minimize the summand matrix in binary multiplication
title_full An efficient algorithmic framework to minimize the summand matrix in binary multiplication
title_fullStr An efficient algorithmic framework to minimize the summand matrix in binary multiplication
title_full_unstemmed An efficient algorithmic framework to minimize the summand matrix in binary multiplication
title_short An efficient algorithmic framework to minimize the summand matrix in binary multiplication
title_sort efficient algorithmic framework to minimize the summand matrix in binary multiplication
topic Binary multiplication
latency optimization
multiplier
summand reduction
Booth’s algorithm
hardware efficiency
url https://www.tandfonline.com/doi/10.1080/00051144.2025.2526261
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