Fixed Arithmetic pipelines

 We obtain the example of multiplication of fixed numbers. The Two fixed-point numbers are added by the ALU using shift and add operations. This sequential implementation makes the multiplication a slow process. If we seem at the multiplication process cautiously, then we examine that this is the process of adding the multiple copies of shifted multiplicands as given below:

Now, we can signify the following phases for the pipeline:

• The first stage produces the partial product of the numbers, which shows the six rows of shifted multiplicands.
• In the second phase, the six numbers are given to the two CSAs merging into four numbers.
• In the third stage, there is a one CSA merging the numbers into 3 numbers.
• In the fourth stage, there is a one number merging three numbers into 2 numbers.
• In the fifth stage, the final two numbers are added through a CPA to get the last product.

These phases have been implemented using CSA tree as shown in Figure:-

                                  Arithmetic pipeline for Multiplication of two 6-digit fixed numbers