From 2293bc5adb82fd82d537178b326df7e6ba26008a Mon Sep 17 00:00:00 2001 From: Xi Zhang Date: Tue, 9 Dec 2025 14:44:24 +0800 Subject: [PATCH] Update Booth multiplier section in 18-microarch.Rmd Revised the Booth multiplier explanation and formula for clarity and hardware implementation suitability. --- 18-microarch.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/18-microarch.Rmd b/18-microarch.Rmd index c7950eb..4e8fd03 100644 --- a/18-microarch.Rmd +++ b/18-microarch.Rmd @@ -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}$$