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    "title": "Booth: multiplying positive and negative binary numbers uniformly",
    "summary": "Booth’s1951 paper gives an add/subtract/shift procedure for signed binary multiplication that avoids a separate sign-detection and correction routine. It adapts a shortcut idea from decimal desk calculators to complementary binary representation.\n\nA computer should multiply two negative numbers just as reliably as two positive ones, without first switching to a separate routine. Booth looks at transitions between neighboring multiplier digits. Those transitions tell the machine whether to add, subtract or simply shift the accumulated partial result. The same pattern handles all sign combinations in the paper’s representation, making the control procedure more uniform.",
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        "description": "Exact target is the original finite signed-binary complement/mod 2 fractional representation and pair-transition add/subtract/right-shift process, including its start/end conventions. Correctness relies on the stated modular arithmetic and shift/register conventions; converting it to bounded-width integer hardware needs explicit sign extension, width and overflow rules. The account does not supply an executable transcription or extreme-value certification. The original motivates simpler sign handling, not a universal speed, energy or circuit-area advantage. It does not imply subquadratic complexity; later modified higher-radix Booth recoding and modern multiplier layouts are separate. Earlier complementary representation, non-restoring division and Rey/Spencer sign-correction work retain credit.",
        "domain": "Computer arithmetic"
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        {
          "citation": "Andrew D. Booth, A Signed Binary Multiplication Technique, QJMAM 4(2),236–240 (1951), institution-hosted original scan",
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          "citation": "Oxford Academic: Booth signed-binary multiplication publication record",
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      "statement": "# Booth: multiplying positive and negative binary numbers uniformly\n\nBooth’s1951 paper gives an add/subtract/shift procedure for signed binary multiplication that avoids a separate sign-detection and correction routine. It adapts a shortcut idea from decimal desk calculators to complementary binary representation.\n\nA computer should multiply two negative numbers just as reliably as two positive ones, without first switching to a separate routine. Booth looks at transitions between neighboring multiplier digits. Those transitions tell the machine whether to add, subtract or simply shift the accumulated partial result. The same pattern handles all sign combinations in the paper’s representation, making the control procedure more uniform.\n\n## Scientific scope\n\nExact target is the original finite signed-binary complement/mod 2 fractional representation and pair-transition add/subtract/right-shift process, including its start/end conventions. Correctness relies on the stated modular arithmetic and shift/register conventions; converting it to bounded-width integer hardware needs explicit sign extension, width and overflow rules. The account does not supply an executable transcription or extreme-value certification. The original motivates simpler sign handling, not a universal speed, energy or circuit-area advantage. It does not imply subquadratic complexity; later modified higher-radix Booth recoding and modern multiplier layouts are separate. Earlier complementary representation, non-restoring division and Rey/Spencer sign-correction work retain credit.\n\n## People and systems\n\nAndrew D. Booth\n\n\n\n## Original sources\n\n- [Andrew D. Booth, A Signed Binary Multiplication Technique, QJMAM 4(2),236–240 (1951), institution-hosted original scan](https://www.ece.ucdavis.edu/~bbaas/281/papers/Booth.1951.pdf)\n- [Oxford Academic: Booth signed-binary multiplication publication record](https://academic.oup.com/qjmam/article-abstract/4/2/236/1874893)\n",
      "summary": "Booth’s1951 paper gives an add/subtract/shift procedure for signed binary multiplication that avoids a separate sign-detection and correction routine. It adapts a shortcut idea from decimal desk calculators to complementary binary representation.\n\nA computer should multiply two negative numbers just as reliably as two positive ones, without first switching to a separate routine. Booth looks at transitions between neighboring multiplier digits. Those transitions tell the machine whether to add, subtract or simply shift the accumulated partial result. The same pattern handles all sign combinations in the paper’s representation, making the control procedure more uniform.",
      "title": "Booth: multiplying positive and negative binary numbers uniformly"
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    "title": "Booth: multiplying positive and negative binary numbers uniformly",
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    "what_changed": "Replaces explicit sign-correction branching with a uniform pair-transition signed binary add/subtract/shift procedure.",
    "scope": "Replaces explicit sign-correction branching with a uniform pair-transition signed binary add/subtract/shift procedure. Exact target is the original finite signed-binary complement/mod 2 fractional representation and pair-transition add/subtract/right-shift process, including its start/end conventions. Correctness relies on the stated modular arithmetic and shift/register conventions; converting it to bounded-width integer hardware needs explicit sign extension, width and overflow rules. The account does not supply an executable transcription or extreme-value certification. The original motivates simpler sign handling, not a universal speed, energy or circuit-area advantage. It does not imply subquadratic complexity; later modified higher-radix Booth recoding and modern multiplier layouts are separate. Earlier complementary representation, non-restoring division and Rey/Spencer sign-correction work retain credit.",
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      {
        "title": "Andrew D. Booth, A Signed Binary Multiplication Technique, QJMAM 4(2),236–240 (1951), institution-hosted original scan",
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