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3.2 Pipelines     continued...

The number of stages is referred to as the depth of the pipeline. As an example of a pipeline, consider the floating point addition of two numbers of the form . One possible breakdown of this function into stages is as follows [33]:

  1. If swap the operands. Find the difference in exponents .
  2. Shift to the right by bits.
  3. Compute the mantissa of the sum by adding and . The exponent of the sum is .
  4. Normalize the sum.
The extra complexity of a pipelined adder pays off when adding long sequences of numbers. Operations at each stage can be done on different pairs of inputs, e.g. one stage can be comparing the exponents in one pair of operands at the same time another stage is adding the mantissas of a different pair of operands.