Sub-expression elimination 96 Sub-expression elimination is a numerical transformation of the constant multiplications that can lead to efficient hardware in terms of area,power and speed. Sub-expression can only be performed on constant multiplications that operate on a common variable. It is essentially the process of examining the shift and add implementations of the constant multiplications and finding redundant operations. Example:a x and b x,where a=001101 and b=011011 can be performed as follows: ■ a*×=000100*×+001001*× ■ b*×=010010*×+001001*×=(001001*x)<<1+(001001*×) The term 001001 x needs to be computed only once. So,multiplications were implemented using 3 shifts and 3 adds as opposed to 5 shifts and 5 adds. 2021年2月 通信抗干扰技术国家重点实验室 32021年2月 通信抗干扰技术国家重点实验室 3 Sub-expression elimination  Sub-expression elimination is a numerical transformation of the constant multiplications that can lead to efficient hardware in terms of area, power and speed.  Sub-expression can only be performed on constant multiplications that operate on a common variable.  It is essentially the process of examining the shift and add implementations of the constant multiplications and finding redundant operations.  Example: a * x and b * x, where a = 001101 and b = 011011 can be performed as follows:  a * x = 000100 * x + 001001 * x  b * x = 010010 * x + 001001 * x = (001001 * x) << 1 +(001001 * x).  The term 001001 * x needs to be computed only once.  So, multiplications were implemented using 3 shifts and 3 adds as opposed to 5 shifts and 5 adds