除法器

除法器(除法算法)是一类算法。给定两个整数 N(分子)和 D(分母),计算它们的和(或)余数。其中某些算法可以通过人工手动计算,而另一些则需要依赖数字电路的设计或软件。[1]

除法算法主要分为两类:慢除法快除法。慢除法在每次迭代的过程中给出结果(商)的一位数字。慢除法包括复原法(restoring)、非复原法(non-restoring)和SRT除法等。快除法从商的一个近似估计开始,并且在每次迭代过程中产生有效位数为最终商的两倍多的中间值。Newton-Raphson和GoldSchmidt属于这一类。

为接下来的讨论的方便,我们有以下标记:

其中

  • N = Numerator (divident) 即“分子”(被除数)
  • D = Denominator (divisor) 即“分母”(除数)

是输入,而输出是

  • Q = Quotient 即“商”
  • R = Remainder 即“余数”

復原的除法器 (restoring)

非復原的除法器 (non-restoring)

SRT演算法的除法器

  1. ^ Division algorithm. Wikipedia. 2018-03-24 [2018-04-14]. (原始内容存档于2019-08-18) (英语). 

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