Explain fixed arithmetic pipelines, Computer Engineering

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Fixed Arithmetic pipelines

We take the illustration of multiplication of fixed numbers. Two fixed point numerals are added by ALU (Arithmetic and logic unit) using shift and add operations. This serial execution makes multiplication a slow process. If we look at the multiplication procedure carefully then we study that this is the procedure of adding the multiple copies of shifted multiplicands as displayed below:

1397_Fixed Arithmetic pipelines.png

Now we can recognize the subsequent phases for pipeline:

The first phase produces the partial product of the numbers that forms the six rows of shifted multiplicands.
In second phase the six numbers are specified to two CSAs merging into four numbers.
In third phase there is a single CSA merging numbers into 3 numbers.
In fourth phase there is a single number merging three numbers in 2 numbers.
In fifth stage the final two numbers are added by a CPA to obtain the final product.

These phases have been implemented by means of CSA tree as displayed in Figure below.

1080_Fixed Arithmetic pipelines 1.png

Figure: Arithmetic pipeline for Multiplication of two 6-digit fixed numbers

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