Fixed arithmetic pipelines, Computer Engineering

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:

                                  10_Fixed Arithmetic pipelines.png

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:-

                                                       2015_Fixed Arithmetic pipelines 1.png


                                  Arithmetic pipeline for Multiplication of two 6-digit fixed numbers

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