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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Signed-digit representation ： ウィキペディア英語版 Signed-digit representation In mathematical notation for numbers, signed-digit representation is a positional system with signed digits; the representation may not be unique. Signed-digit representation can be used to accomplish fast addition of integers because it can eliminate chains of dependent carries.〔Dhananjay Phatak, I. Koren, Hybrid Signed-Digit Number Systems: A Unified Framework for Redundant Number Representations with Bounded Carry Propagation Chains, 1994, ()〕 In the binary numeral system, a special case signed-digit representation is the ''non-adjacent form'', which can offer speed benefits with minimal space overhead. Challenges in calculation stimulated early authors Colson (1726) and Cauchy (1840) to use signed-digit representation. The further step of replacing negated digits with new ones was suggested by Selling (1887) and Cajori (1928). ==Balanced form== In balanced form, the digits are drawn from a range $\backslash scriptstyle\; -k$ to $\backslash scriptstyle\; (b\; \backslash ,-\backslash ,\; 1)\; \backslash ,-\backslash ,\; k$, where typically $\backslash scriptstyle\; k\; ~=~\; \backslash left\backslash lfloor\backslash frac\backslash right\backslash rfloor$. For balanced forms, odd base numbers are advantageous. With an odd base number, truncation and rounding become the same operation, and all the digits except 0 are used in both positive and negative form. A notable example is balanced ternary, where the base is $\backslash scriptstyle\; b\; ~=~\; 3$, and the numerals have the values −1, 0 and +1 (rather than 0, 1, and 2 as in the standard ternary numeral system). Balanced ternary uses the minimum number of digits in a balanced form. ''Balanced decimal'' uses digits from −5 to +4. Balanced base nine, with digits from −4 to +4 provides the advantages of an odd-base balanced form with a similar number of digits, and is easy to convert to and from balanced ternary. Other notable examples include Booth encoding and non-adjacent form, both of which use a base of $\backslash scriptstyle\; b\; ~=~\; 2$, and both of which use numerals with the values −1, 0, and +1 (rather than 0 and 1 as in the standard binary numeral system). 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「Signed-digit representation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.