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Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation. The algorithm was invented by Andrew Donald Booth in 1950 while doing research on crystallography at Birkbeck College in Bloomsbury, London. Booth used desk calculators that were faster at shifting than adding and created the algorithm to increase their speed. Booth's algorithm is of interest in the study of computer architecture. ==The algorithm== Booth's algorithm examines adjacent pairs of bits of the ''N''-bit multiplier ''Y'' in signed two's complement representation, including an implicit bit below the least significant bit, ''y''-1 = 0. For each bit ''y''''i'', for ''i'' running from 0 to ''N''-1, the bits ''y''''i'' and ''y''''i''-1 are considered. Where these two bits are equal, the product accumulator ''P'' is left unchanged. Where ''y''''i'' = 0 and ''y''''i''-1 = 1, the multiplicand times 2''i'' is added to ''P''; and where ''y''i = 1 and ''y''i-1 = 0, the multiplicand times 2''i'' is subtracted from ''P''. The final value of ''P'' is the signed product. The multiplicand and product are not specified; typically, these are both also in two's complement representation, like the multiplier, but any number system that supports addition and subtraction will work as well. As stated here, the order of the steps is not determined. Typically, it proceeds from LSB to MSB, starting at ''i'' = 0; the multiplication by 2''i'' is then typically replaced by incremental shifting of the ''P'' accumulator to the right between steps; low bits can be shifted out, and subsequent additions and subtractions can then be done just on the highest ''N'' bits of ''P''.〔 〕 There are many variations and optimizations on these details. The algorithm is often described as converting strings of 1's in the multiplier to a high-order +1 and a low-order –1 at the ends of the string. When a string runs through the MSB, there is no high-order +1, and the net effect is interpretation as a negative of the appropriate value. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Booth's multiplication algorithm」の詳細全文を読む スポンサード リンク
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