Problem #7 A processor chip is used for applications in which 30% of the executi

Question

Problem #7 A processor chip is used for applications in which 30% of the execution time is spent on floating- point addition, 60% on floating-point multiplication, and 10% on floating-point division. For the new model of the processor, the design team has come up with three possible enhancements, each costing roughly the same in design effort and manufacturing. Which one of these enhancements will be chosen? Show all your work to get full credit. (i) Redesign the floating-point adder to make it twice as fast. (ii) Redesign the floating-point multiplier to make it three times as fast. (iii) Redesign the floating-point divider to make it ten times as fast. (iv) Redesign both the floating-point adder and multiplier to make each one two times as fast.

Explanation / Answer

Lets assume for the shake of problem that we have a total time of 100 seconds. Then according to the problem statement :

adding time = 30 seconds

multiplication time = 60 seconds

division time = 10 seconds

Now going through each of the new updates one by one:  

(i) Redesign the floating-point adder to make it twice as fast

So now addition will be twice fast, Therefore time taken for addition is

current addition time / 2 = 30 seconds / 2 = 15 seconds

Therefore total time saved = 30 seconds - 15 seconds = 15 seconds

Which in percentage is (15 seconds / 100 seconds) * 100 = 15 %

(ii) Redesign the floating-point multiplier to make it three times as fast

So now multiplication will be thrice as fast, Therefore time taken for multiplication is

Current multiplication time / 3 = 60 seconds / 3 = 20 seconds

Therefore total time saved = 60 seconds - 20 seconds = 40 seconds

Which in percentage is (40 seconds / 100 seconds) * 100 = 40 %

(iii) Redesign the floating point divider to make it ten times as fast

So now division will be 10 times as fast, Therefore time taken for division is

current division time / 10 = 10 seconds / 10 = 1 second

Therefore totaltime saved = 10 seconds - 1 second = 9 seconds

which in percentage is (9 seconds / 100 seconds) * 100 = 9 %

(iv) Redesign both the floating-point adder and multiplier to make each one two times as fast

So now addition will be twice fast and multiplication will also be twice as fast,

Therefore time taken for addition is

current addition time / 2 = 30 seconds / 2 = 15 seconds

Therefore time saved = 30 seconds - 15 seconds = 15 seconds

And time taken for multiplication is

Current multiplication time / 2 = 60 seconds / 2 = 30 seconds

Therefore time saved = 60 seconds - 30 seconds = 30 seconds

Therefore total time saved = time saved in addition + time saved in multiplication

= 15 seconds + 30 seconds

= 45 seconds

which in percentage is (45 seconds/ 100 seconds) * 100 seconds = 45 %

Now from above, it is cleare that the option (iv) makes the processor chip most fast.

Therefore I will chose the (iv) option.

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