Structure and Principles of Operation of a Quaternion VLSI Multiplier

The paper presents the original structure of a processing unit for multiplying quaternions. The idea of organizing the device is based on the use of fast Hadamard transform blocks. The operation principles of such a device are described. Compared to direct quaternion multiplication, the developed al...

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Main Authors: Aleksandr Cariow, Mariusz Naumowicz, Andrzej Handkiewicz
Format: Article
Language:English
Published: MDPI AG 2024-09-01
Series:Applied Sciences
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Online Access:https://www.mdpi.com/2076-3417/14/18/8123
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author Aleksandr Cariow
Mariusz Naumowicz
Andrzej Handkiewicz
author_facet Aleksandr Cariow
Mariusz Naumowicz
Andrzej Handkiewicz
author_sort Aleksandr Cariow
collection DOAJ
description The paper presents the original structure of a processing unit for multiplying quaternions. The idea of organizing the device is based on the use of fast Hadamard transform blocks. The operation principles of such a device are described. Compared to direct quaternion multiplication, the developed algorithm significantly reduces the number of multiplication and addition operations. Hardware implementations of the developed structure, in FPGA and ASIC, are presented. The FPGA blocks were implemented in the Vivado environment. The ASICs were designed using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>130</mn><mspace width="3.33333pt"></mspace><mi>nm</mi></mrow></semantics></math></inline-formula> technology. The developed scripts in VHDL are available in the GitHub repository.
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institution OA Journals
issn 2076-3417
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publishDate 2024-09-01
publisher MDPI AG
record_format Article
series Applied Sciences
spelling doaj-art-b0f84f5b387b41ae8e4bc7d5a8bf8de62025-08-20T01:55:58ZengMDPI AGApplied Sciences2076-34172024-09-011418812310.3390/app14188123Structure and Principles of Operation of a Quaternion VLSI MultiplierAleksandr Cariow0Mariusz Naumowicz1Andrzej Handkiewicz2Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, 70-310 Szczecin, PolandFaculty of Computing, Poznań University of Technology, ul. Piotrowo 3a, 60-965 Poznań, PolandFaculty of Technology, The Jacob of Paradise University, 66-400 Gorzów Wielkopolski, PolandThe paper presents the original structure of a processing unit for multiplying quaternions. The idea of organizing the device is based on the use of fast Hadamard transform blocks. The operation principles of such a device are described. Compared to direct quaternion multiplication, the developed algorithm significantly reduces the number of multiplication and addition operations. Hardware implementations of the developed structure, in FPGA and ASIC, are presented. The FPGA blocks were implemented in the Vivado environment. The ASICs were designed using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>130</mn><mspace width="3.33333pt"></mspace><mi>nm</mi></mrow></semantics></math></inline-formula> technology. The developed scripts in VHDL are available in the GitHub repository.https://www.mdpi.com/2076-3417/14/18/8123hypercomplex numbersquaternion multiplierfast algorithmmatrix–vector multiplicationhardware implementationFPGA
spellingShingle Aleksandr Cariow
Mariusz Naumowicz
Andrzej Handkiewicz
Structure and Principles of Operation of a Quaternion VLSI Multiplier
Applied Sciences
hypercomplex numbers
quaternion multiplier
fast algorithm
matrix–vector multiplication
hardware implementation
FPGA
title Structure and Principles of Operation of a Quaternion VLSI Multiplier
title_full Structure and Principles of Operation of a Quaternion VLSI Multiplier
title_fullStr Structure and Principles of Operation of a Quaternion VLSI Multiplier
title_full_unstemmed Structure and Principles of Operation of a Quaternion VLSI Multiplier
title_short Structure and Principles of Operation of a Quaternion VLSI Multiplier
title_sort structure and principles of operation of a quaternion vlsi multiplier
topic hypercomplex numbers
quaternion multiplier
fast algorithm
matrix–vector multiplication
hardware implementation
FPGA
url https://www.mdpi.com/2076-3417/14/18/8123
work_keys_str_mv AT aleksandrcariow structureandprinciplesofoperationofaquaternionvlsimultiplier
AT mariusznaumowicz structureandprinciplesofoperationofaquaternionvlsimultiplier
AT andrzejhandkiewicz structureandprinciplesofoperationofaquaternionvlsimultiplier