In this problem, you will explore the design of a 32-bit floating-point multiplier. The multiplier has two 32-bit floating-point inputs and produces a 32-bit floating-point output. You may consider positive numbers only and use round toward zero (truncate). You may also ignore the special cases given in Table 5.2. 

(a) Write the steps necessary to perform 32-bit floating-point multiplication.
(b) Sketch the schematic of a 32-bit floating-point multiplier.
(c) Design a 32-bit floating-point multiplier in an HDL. Simulate and test your multiplier to prove to a skeptic that it functions correctly.

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Table 5.2 IEEE 754 floating-point notations for 0, too, and NaN Number Sign Exponent Fraction X 00000000 00000000000000000000000 11111111 00000000000000000000000 00 1. 11111111 00000000000000000000000 -00 NaN X 11111111 Non-zero