<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">kaz29</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник Казахстанско-Британского технического университета</journal-title><trans-title-group xml:lang="en"><trans-title>Herald of the Kazakh-British Technical University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1998-6688</issn><issn pub-type="epub">2959-8109</issn><publisher><publisher-name>Казахстанско-Британский Технический Университет</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.55452/1998-6688-2026-23-3-188-203</article-id><article-id custom-type="elpub" pub-id-type="custom">kaz29-3185</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>КОМПЬЮТЕРНЫЕ НАУКИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>COMPUTER SCIENCE</subject></subj-group></article-categories><title-group><article-title>АРХИТЕКТУРА ЦЕЛОЧИСЛЕННОГО ДЕЛИТЕЛЯ С ОДНОВРЕМЕННЫМ ФОРМИРОВАНИЕМ ТРЕХ РАЗРЯДОВ ЧАСТНОГО ЗА ШАГ</article-title><trans-title-group xml:lang="en"><trans-title>A SEQUENTIAL INTEGER DIVIDER WITH THREE-BIT QUOTIENT DIGIT GENERATION</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9326-9476</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Тынымбаев</surname><given-names>С.</given-names></name><name name-style="western" xml:lang="en"><surname>Tynymbayev</surname><given-names>S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Профессор</p><p>Алматы</p></bio><bio xml:lang="en"><p>Professor</p><p>Almaty</p></bio><email xlink:type="simple">s.tynymbayev@iitu.edu.kz</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0001-7277-5492</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Маманова</surname><given-names>С. Е.</given-names></name><name name-style="western" xml:lang="en"><surname>Mamanova</surname><given-names>S. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Докторант</p><p>Алматы</p></bio><bio xml:lang="en"><p>PhD Candidate</p><p>Almaty</p></bio><email xlink:type="simple">s.mamanova@iitu.edu.kz</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5196-8252</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Сқабылов</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Skabylov</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>PhD</p><p>Алматы</p></bio><bio xml:lang="en"><p>PhD</p><p>Almaty</p></bio><email xlink:type="simple">Alisher.skabylov@kaznu.edu.kz</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-2657-3697</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Чинибаева</surname><given-names>Т. Т.</given-names></name><name name-style="western" xml:lang="en"><surname>Chinibayeva</surname><given-names>T. T.</given-names></name></name-alternatives><bio xml:lang="ru"><p>PhD</p><p>Алматы</p></bio><bio xml:lang="en"><p>PhD</p><p>Almaty</p></bio><email xlink:type="simple">t.temirbolatova@iitu.edu.kz</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0008-1884-4662</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Жексебай</surname><given-names>Д. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Zhexebay</surname><given-names>D. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>PhD</p><p>Алматы</p></bio><bio xml:lang="en"><p>PhD</p><p>Almaty</p></bio><email xlink:type="simple">zhexebay92@gmail.com</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Международный университет информационных технологий</institution><country>Казахстан</country></aff><aff xml:lang="en"><institution>International Information Technology University</institution><country>Kazakhstan</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Казахский национальный университет им. аль-Фараби</institution><country>Казахстан</country></aff><aff xml:lang="en"><institution>Al-Farabi Kazakh National University</institution><country>Kazakhstan</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>25</day><month>09</month><year>2026</year></pub-date><volume>23</volume><issue>3</issue><fpage>188</fpage><lpage>203</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Тынымбаев С., Маманова С.Е., Сқабылов А.А., Чинибаева Т.Т., Жексебай Д.М., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Тынымбаев С., Маманова С.Е., Сқабылов А.А., Чинибаева Т.Т., Жексебай Д.М.</copyright-holder><copyright-holder xml:lang="en">Tynymbayev S., Mamanova S.E., Skabylov A.A., Chinibayeva T.T., Zhexebay D.M.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://vestnik.kbtu.edu.kz/jour/article/view/3185">https://vestnik.kbtu.edu.kz/jour/article/view/3185</self-uri><abstract><p>Операция целочисленного деления является одной из наиболее ресурсоёмких арифметических опера­ций в цифровых вычислительных системах. Традиционные последовательные делители формируют один разряд частного за такт, что требует n тактов для n-разрядного деления. В данной работе предлагается ар­хитектура последовательного целочисленного делителя, обеспечивающая одновременное формирование трех разрядов частного за один тактовый цикл (что соответствует основанию radix-8). Устройство включает регистр делимого (РгА), формирователь кратных делителю (БФКД), формирователь частичных остатков и разрядов частного (ФЧОиРЧ) и блок синхронизации (БС). В отличие от классических SRT-делителей с избыточным представлением и таблицами выбора цифры частного, предложенная архитектура использует точное сравнение частичного остатка с предвычисленными кратными делителю B-7B, что устраняет рост таблицы выбора при увеличении основания. Архитектура описана на языке Verilog HDL и верифицирова­на на ПЛИС Xilinx Artix-7 в среде Vivado. Прототип для 12-разрядного делимого и 6-разрядного делителя занимает 158 LUT и 50 триггеров, достигает максимальной тактовой частоты 134,6 МГц и подтвержден комплексом из десяти тестов; деление выполняется за два тактовых цикла. Архитектура ориентирована на применение в высокоскоростных цифровых вычислителях и специализированных процессорах.</p></abstract><trans-abstract xml:lang="en"><p>Integer division remains one of the most computationally demanding arithmetic operations in digital computing systems. Conventional sequential dividers produce one quotient bit per clock cycle, requiring n cycles for an n-bit division. This paper proposes an architecture for a sequential integer divider capable of simultaneously generating three quotient bits per clock cycle. The proposed device comprises a dividend register (DR), a divisor multiples generator (DMG), a partial remainder and quotient digit generator (PRQDG), and a synchronization unit (SU). Unlike classical SRT dividers, which rely on a redundant quotient representation and quotient-digit selection tables, the proposed architecture performs an exact comparison of the partial remainder against the precomputed divisor multiples B-7B, thereby eliminating the growth of the selection table as the radix increases. The architecture is described in Verilog HDL and verified on a Xilinx Artix-7 FPGA using the Vivado design suite. The prototype for a 12-bit dividend and a 6-bit divisor occupies 158 LUTs and 50 flip-flops, attains a maximum clock frequency of 134.6 MHz, and is confirmed by a suite of ten tests; a division is completed in two clock cycles. The architecture is intended for use in high-speed digital computing units and specialized processors.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>целочисленное деление</kwd><kwd>кратные делителю</kwd><kwd>формирователь остатков</kwd><kwd>формирова¬тель разрядов частного</kwd><kwd>последовательный делитель</kwd><kwd>radix-8</kwd><kwd>ПЛИС</kwd><kwd>Verilog HDL</kwd></kwd-group><kwd-group xml:lang="en"><kwd>integer division</kwd><kwd>divisor multiples</kwd><kwd>remainder generator</kwd><kwd>quotient digit generator</kwd><kwd>sequential divider</kwd><kwd>radix-8</kwd><kwd>FPGA</kwd><kwd>Verilog HDL</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Wei, X., Yang, Y., Chen, J. A Low-Latency Divider Design for Embedded Processors. Sensors, 22, 2471 (2022). https://doi.org/10.3390/s22072471</mixed-citation><mixed-citation xml:lang="en">Wei, X., Yang, Y., Chen, J. A Low-Latency Divider Design for Embedded Processors. Sensors, 22, 2471 (2022). https://doi.org/10.3390/s22072471</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Mehta, B., Talukdar, J., Gajjar, S. High speed SRT divider for intelligent embedded system. In Proc. 2017 Int. Conf. on Soft Computing and its Engineering Applications (icSoftComp) (Changa, India, 2017), pp. 1–5. https://doi.org/10.1109/ICSOFTCOMP.2017.8280077</mixed-citation><mixed-citation xml:lang="en">Mehta, B., Talukdar, J., Gajjar, S. High speed SRT divider for intelligent embedded system. In Proc. 2017 Int. Conf. on Soft Computing and its Engineering Applications (icSoftComp) (Changa, India, 2017), pp. 1–5. https://doi.org/10.1109/ICSOFTCOMP.2017.8280077</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Patankar, U.S., Flores, M.E., Koel, A. Division Algorithms—from Past to Present Chance to Improve Area Time and Complexity for Digital Applications. In Proceedings of the 2020 IEEE Latin America Electron Devices Conference (LAEDC) (San Jose, Costa Rica, 2020), pp. 1–4.</mixed-citation><mixed-citation xml:lang="en">Patankar, U.S., Flores, M.E., Koel, A. Division Algorithms—from Past to Present Chance to Improve Area Time and Complexity for Digital Applications. In Proceedings of the 2020 IEEE Latin America Electron Devices Conference (LAEDC) (San Jose, Costa Rica, 2020), pp. 1–4.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Angioli, M., Barbirotta, M., Cheikh, A., Mastrandrea, A., Menichelli, F., Jamili, S., Olivieri, M. Design, Implementation and Evaluation of a New Variable Latency Integer Division Scheme. IEEE Transactions on Computers, 73 (7), 1767–1779 (2024). https://doi.org/10.1109/TC.2024.3386060</mixed-citation><mixed-citation xml:lang="en">Angioli, M., Barbirotta, M., Cheikh, A., Mastrandrea, A., Menichelli, F., Jamili, S., Olivieri, M. Design, Implementation and Evaluation of a New Variable Latency Integer Division Scheme. IEEE Transactions on Computers, 73 (7), 1767–1779 (2024). https://doi.org/10.1109/TC.2024.3386060</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Murillo, R., Villalba-Moreno, J., Del Barrio, A., Botella, G. Digit-Recurrence Posit Division. arXiv (2025). https://doi.org/10.48550/arXiv.2511.02494</mixed-citation><mixed-citation xml:lang="en">Murillo, R., Villalba-Moreno, J., Del Barrio, A., Botella, G. Digit-Recurrence Posit Division. arXiv (2025). https://doi.org/10.48550/arXiv.2511.02494</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Nannarelli, A., Lang, T. Low-Power Division: Comparison among Implementations of Radix 4, 8 and 16. In Proceedings of the 14th IEEE Symposium on Computer Arithmetic (Adelaide, Australia, 1999), pp. 149–156.</mixed-citation><mixed-citation xml:lang="en">Nannarelli, A., Lang, T. Low-Power Division: Comparison among Implementations of Radix 4, 8 and 16. In Proceedings of the 14th IEEE Symposium on Computer Arithmetic (Adelaide, Australia, 1999), pp. 149–156.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Nikmehr, H., Phillips, B., Lim, C.C. A Fast Radix-4 Floating-Point Divider with Quotient Digit Selection by Comparison Multiples. The Computer Journal, 50 (1), 81–92 (2007). https://doi.org/10.1093/comjnl/bxl048</mixed-citation><mixed-citation xml:lang="en">Nikmehr, H., Phillips, B., Lim, C.C. A Fast Radix-4 Floating-Point Divider with Quotient Digit Selection by Comparison Multiples. The Computer Journal, 50 (1), 81–92 (2007). https://doi.org/10.1093/comjnl/bxl048</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Zhou, X., Shen, R., He, P., Gao, H. Optimization and Implementation of SRT-16 Floating-Point Divider Based on FPGA. In Proceedings of the 5th International Seminar on Artificial Intelligence, Networking and Information Technology (AINIT) (2024), pp. 2019–2023.</mixed-citation><mixed-citation xml:lang="en">Zhou, X., Shen, R., He, P., Gao, H. Optimization and Implementation of SRT-16 Floating-Point Divider Based on FPGA. In Proceedings of the 5th International Seminar on Artificial Intelligence, Networking and Information Technology (AINIT) (2024), pp. 2019–2023.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Baesler, M., Voigt, S.O. Analysis of Fast Radix-10 Digit Recurrence Algorithms for Fixed-Point and Floating-Point Dividers on FPGAs. International Journal of Reconfigurable Computing, 453173 (2013). https://doi.org/10.1155/2013/453173</mixed-citation><mixed-citation xml:lang="en">Baesler, M., Voigt, S.O. Analysis of Fast Radix-10 Digit Recurrence Algorithms for Fixed-Point and Floating-Point Dividers on FPGAs. International Journal of Reconfigurable Computing, 453173 (2013). https://doi.org/10.1155/2013/453173</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Zhexebay, D., Mamanova, S., Karibayev, B., et al. Pipelined Divider with Precomputed Multiples of Divisor. Electronics, 15 (1), 110 (2026). https://doi.org/10.3390/electronics15010110</mixed-citation><mixed-citation xml:lang="en">Zhexebay, D., Mamanova, S., Karibayev, B., et al. Pipelined Divider with Precomputed Multiples of Divisor. Electronics, 15 (1), 110 (2026). https://doi.org/10.3390/electronics15010110</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Temel, M. Formal Verification of Booth Radix-8 and Radix-16 Multipliers. In Proc. 2024 Design, Automation &amp; Test in Europe Conf. &amp; Exhibition (DATE) (IEEE, 2024).</mixed-citation><mixed-citation xml:lang="en">Temel, M. Formal Verification of Booth Radix-8 and Radix-16 Multipliers. In Proc. 2024 Design, Automation &amp; Test in Europe Conf. &amp; Exhibition (DATE) (IEEE, 2024).</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Kornerup, P. Digit selection for SRT division and square root. IEEE Transactions on Computers, 54 (3), 294–303 (2005). https://doi.org/10.1109/TC.2005.52</mixed-citation><mixed-citation xml:lang="en">Kornerup, P. Digit selection for SRT division and square root. IEEE Transactions on Computers, 54 (3), 294–303 (2005). https://doi.org/10.1109/TC.2005.52</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Amin, A., Shinwari, W. High-Radix Multiplier-Dividers: Theory, Design, and Hardware. IEEE Transactions on Computers, 59 (7), 1009–1022 (2010). https://doi.org/10.1109/TC.2010.78</mixed-citation><mixed-citation xml:lang="en">Amin, A., Shinwari, W. High-Radix Multiplier-Dividers: Theory, Design, and Hardware. IEEE Transactions on Computers, 59 (7), 1009–1022 (2010). https://doi.org/10.1109/TC.2010.78</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Oberman, S.F., Flynn, M.J. Division algorithms and implementations. IEEE Transactions on Computers, 46 (8), 833–854 (1997). https://doi.org/10.1109/12.618254</mixed-citation><mixed-citation xml:lang="en">Oberman, S.F., Flynn, M.J. Division algorithms and implementations. IEEE Transactions on Computers, 46 (8), 833–854 (1997). https://doi.org/10.1109/12.618254</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Nannarelli, A. Digit Recurrence Division Algorithms and Implementations (Ph.D. thesis, University of Pisa, 1996).</mixed-citation><mixed-citation xml:lang="en">Nannarelli, A. Digit Recurrence Division Algorithms and Implementations (Ph.D. thesis, University of Pisa, 1996).</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Patankar, U.S., Koel, A. Review of basic classes of dividers based on division algorithm. IEEE Access, 9, 23035–23069 (2021). https://doi.org/10.1109/ACCESS.2021.3055735</mixed-citation><mixed-citation xml:lang="en">Patankar, U.S., Koel, A. Review of basic classes of dividers based on division algorithm. IEEE Access, 9, 23035–23069 (2021). https://doi.org/10.1109/ACCESS.2021.3055735</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Harris, D.L., Oberman, S.F., Horowitz, M.A. SRT Division Architectures and Implementations. In Proc. 13th IEEE Symp. on Computer Arithmetic (1997), pp. 18–25. https://doi.org/10.1109/ARITH.1997.614875</mixed-citation><mixed-citation xml:lang="en">Harris, D.L., Oberman, S.F., Horowitz, M.A. SRT Division Architectures and Implementations. In Proc. 13th IEEE Symp. on Computer Arithmetic (1997), pp. 18–25. https://doi.org/10.1109/ARITH.1997.614875</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Anane, M., Bessalah, H., Issad, M., Anane, N., Salhi, H. Higher radix and redundancy factor for floating point SRT division. IEEE Transactions on VLSI Systems, 16 (6), 774–779 (2008). https://doi.org/10.1109/TVLSI.2008.2001058</mixed-citation><mixed-citation xml:lang="en">Anane, M., Bessalah, H., Issad, M., Anane, N., Salhi, H. Higher radix and redundancy factor for floating point SRT division. IEEE Transactions on VLSI Systems, 16 (6), 774–779 (2008). https://doi.org/10.1109/TVLSI.2008.2001058</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Montuschi, P., Nannarelli, A. Digital arithmetic: Division algorithms. In Encyclopedia of Computer Science and Technology (New York: Taylor &amp; Francis, 2017), pp. 348–363.</mixed-citation><mixed-citation xml:lang="en">Montuschi, P., Nannarelli, A. Digital arithmetic: Division algorithms. In Encyclopedia of Computer Science and Technology (New York: Taylor &amp; Francis, 2017), pp. 348–363.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Matthews, J., Zhang, Z., Chen, Z. Rethinking integer divider design for FPGA-based soft processors. In Proceedings of the 2019 IEEE 27th Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM) (San Diego, CA, USA, 2019), pp. 115–122.</mixed-citation><mixed-citation xml:lang="en">Matthews, J., Zhang, Z., Chen, Z. Rethinking integer divider design for FPGA-based soft processors. In Proceedings of the 2019 IEEE 27th Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM) (San Diego, CA, USA, 2019), pp. 115–122.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
