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99 votes
99 votes
Suppose the functions $F$ and $G$ can be computed in $5$ and $3$ nanoseconds by functional units $U_{F}$ and $U_{G}$, respectively. Given two instances of $U_{F}$ and two instances of $U_{G}$, it is required to implement the computation $F(G(X_{i}))$ for $1 \leq i \leq 10$. Ignoring all other delays, the minimum time required to complete this computation is ____________ nanoseconds.
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12 Answers

14 votes
14 votes

Using concepts of pipelining, answer comes out to be 28.

10 votes
10 votes

We can use two instances of both F and G at same time but F depends on G.So,first compute G then F.

6 votes
6 votes
$10$ instructions using two pair of functional units will take time equivalent to $5$ instructions.

For a pipeline with $k$ stages & $n$ instructions.

$T_{pipeline} \space =\space \sum_{i=1}^{k} \delta_{i} \space + \space (n-1)*\delta_{max}$ where $\delta_{i}$ is delay of $i_{th}$ stage.

$\implies T_{pipeline} \space = 3+5 + \space (5-1)*5 = 28 $
4 votes
4 votes

This is pipeline concept

two unit says we have to pipelines with same functionality.we can start both of them at same time.

Lets distribute i's values 1 to 5 for pipeline1...6 to 10 for pipeline2...

T1=(3+5)+(4*5)=28=T2 

T1=Time required for pipeline1

T2=Time required for pipeline2

Parallel running so answer should be 28.

Answer:

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