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2 changes: 1 addition & 1 deletion 18-microarch.Rmd
Original file line number Diff line number Diff line change
Expand Up @@ -632,7 +632,7 @@ Booth乘法器由英国的Booth夫妇提出。按照8.3.1小节中的补码乘

Booth一位乘变换的公式推导如下:

$$\begin{aligned}&\quad(-y_{7}\times 2^{7}+y_{6}\times 2……{6}+\ldots +y_{1}\times 2^{1}+y_{0}\times 2^{0})\\
$$\begin{aligned}&\quad(-y_{7}\times 2^{7}+y_{6}\times 2^{6}+\ldots +y_{1}\times 2^{1}+y_{0}\times 2^{0})\\
&=(-y_{7}\times 2^{7}+(y_{6}\times 2^{7}-y_{6}\times 2^{6})+(y_{5}\times 2^{6}-y_{5}\times 2^{5})+\ldots + \\ &\quad(y_{1}\times 2^{2}-y_{1}\times 2^{1})+(y_{0}\times 2^{1}-y_{0}\times 2^{0})+(0\times 2^{0}))\\
&=(y_{6}-y_{7})\times 2^{7}+(y_{5}-y_{6})\times 2^{6}+\ldots +(y_{0}-y_{1})\times 2^{1}+(y_{-1}-y_{0})\times 2^{0}\end{aligned}$$

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