V2EX positional notation

Positional Notation

Definition / 释义

(数学)位值记数法/位置记数法:一种记数体系,数字中每一位的数值由“数字本身 + 所在位置(位权,如个位、十位、百位)”共同决定。常见例子是十进制与二进制等。(另有“非位值记数法”,如罗马数字。)

Pronunciation / 发音

/pznl noten/

Examples / 例句

In decimal positional notation, the digit 7 in 70 means seven tens.
在十进制位值记数法中,70 里的 7 表示“七个十”。

Computers rely on positional notation in base 2, where shifting a bit left multiplies the value by two.
计算机依赖二进制位值记数法,在其中把一位二进制数左移会使数值乘以 2。

Etymology / 词源

positional 来自 position(位置),强调“由位置决定”;notation 指“记号/表示法”。合起来就是“用位置来决定数值的表示法”。这一概念常与“进位制(base)”一起出现,例如十进制、二进制、十六进制等。

Related Words / 相关词

Literary Works / 文学作品

  • 《Liber Abaci》(Fibonacci,1202):介绍并推广当时欧洲尚不普及的“印度阿拉伯数字体系”,其核心就是位值记数思想。
  • 《Gdel, Escher, Bach: An Eternal Golden Braid》(Douglas Hofstadter):在讨论形式系统与编码时提及不同进制与位值表示的直观意义。
  • 《A History of Mathematics》(Carl B. Boyer & Uta C. Merzbach):讲述数字系统的历史发展,包含位值记数法在数学传播与计算便利性上的重要性。
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