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GATE | GATE-IT-2004 | Question 50

  • Last Updated : 19 Nov, 2018

In an enhancement of a design of a CPU, the speed of a floating point unit has been increased by 20% and the speed of a fixed point unit has been increased by 10%. What is the overall speedup achieved if the ratio of the number of floating point operations to the number of fixed point operations is 2:3 and the floating point operation used to take twice the time taken by the fixed point operation in the original design?
(A) 1.155
(B) 1.185
(C) 1.255
(D) 1.285

Answer: (A)

Explanation: Speed Up = Time taken in original design / Time taken in enhanced design

In original design:
Ratio of floating point operations to fixed point operations = 2:3
Therefore let floating point operations be 2n and fixed point operations be 3n.

Ratio of time taken by floating point operation to fixed point operation =2:1
Therefore let time taken by floating point operation be 2t and by fixed point 
operation be t.

Time taken by the original design = (2n * 2t) + (3n * t) = 7nt 
In Enhanced design:
As the speed of the floating point operation is increased by 
20%  (1.2 * original speed) time taken for a floating point operation 
would be 83.33%  of the original time (original time/1.2)(This is because CPU 
speed(S) is inversely proportional to execution time (T) hence if speed becomes 
1.2S time would become T/1.2 )

Similarly for a of fixed point operation speed is increased by 10% (1.1 * original 
speed), it means the time taken now would be 90.91% of the original time 
(original time / 1.1) taken in case of fixed point operation.

Time taken by enhanced design= (2n * 2t /1.2) + (3n * t /1.1) = 6.06nt

Speed up= 7nt / 6.06nt = 1.155

This explanation has been contributed by Yashika Arora.

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