Suppose A = E4 and B = 5E (both in hexadecimal). Show the step by step result mu

Question

Suppose A = E4 and B = 5E (both in hexadecimal). Show the step by step result multiplying A and B, using the multiplier hardware shown in Fig. 1. Assume A and B are 8-bit unsigned numbers, stored in hexadecimal format. Suppose for an 8-bit number, each step of operation (either addition or shift) takes 2ns. Please calculate the time necessary to perform a multiply using the approach given in Fig. 1. Assume the registers have been initialized. In hardware, please note that the shifts of the multiplicand and multiplier can be done simultaneously.

Explanation / Answer

A = E4

B = E5

A = E4 = 228 base 10 = 1110 0100 base 2

B = E5 = 229 base 10 = 1110 0101 base 2

* = multiplication

Let C = A * B

Understanding the Arithmetic Logical Unit (ALU) the key component of the hexadecimal multiplier:

E4

E5

1

1

1

0

0

1

0

0

1

1

1

0

0

1

0

1

1

1

0

0

1

0

1

1

1

1

1

1

0

1

0

0

E4

E5

1

1

1

0

0

1

0

0

1

1

1

0

0

1

0

1

1

1

0

0

1

0

1

1

1

1

1

1

0

1

0

0

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