|
A negative base (or negative radix) may be used to construct a non-standard positional numeral system. Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base is equal to for some natural number (''r ≥ 2''). Negative-base systems can accommodate all the same numbers as standard place-value systems, but both positive and negative numbers are represented without the use of a minus sign (or, in computer representation, a sign bit); this advantage is countered by an increased complexity of arithmetic operations. The need to store the information normally contained by a negative sign often results in a negative-base number being one digit longer than its positive-base equivalent. The common names for negative-base positional numeral systems are formed by prefixing ''nega-'' to the name of the corresponding positive-base system; for example, negadecimal (base −10) corresponds to decimal (base 10), negabinary (base −2) to binary (base 2), and negaternary (base −3) to ternary (base 3).〔. Knuth mentions both negabinary and negadecimal.〕〔The negaternary system is discussed briefly in .〕 ==Example== Consider what is meant by the representation ''12,243'' in the negadecimal system, whose base is −10: Since 10,000 + (−2,000) + 200 + (−40) + 3 = 8,163, the representation ''12,243'' in negadecimal notation is equivalent to ''8,163'' in decimal notation. While ''-8,163'' in decimal would be written ''9,977'' in negadecimal. 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「Negative base」の詳細全文を読む スポンサード リンク
|