Question

An application executes \( 6.4 \times 10^8 \) number of instructions in 6.3 seconds. There are four types of instructions, the details of which are given in the table. The duration of a clock cycle in nanoseconds is ___________. (rounded off to one decimal place) \begin{center} \begin{tabular}{|c|c|c|} \hline Instruction type & Clock cycles per instruction (CPI) & Number of instructions executed
\hline Branch & 2 & \( 2.25 \times 10^8 \)
Load & 5 & \( 1.20 \times 10^8 \)
Store & 4 & \( 1.65 \times 10^8 \)
Arithmetic & 3 & \( 1.30 \times 10^8 \)
\hline \end{tabular} \end{center}

Hint:

To calculate clock cycle time, first determine total clock cycles using CPI values, then compute cycle time as the inverse of the clock frequency.

Answer 1

Correct Answer: 3

The processor executes four categories of instructions, each contributing a certain number of clock cycles. Adding all these contributions gives a total of \(2.10 \times 10^9\) cycles for the complete program.

Since the entire execution finishes in \(6.3\) seconds, the average number of cycles completed per second is:

\(\dfrac{2.10 \times 10^9}{6.3} = 3.33 \times 10^8\)

This represents the clock rate of the processor. The duration of one clock cycle is therefore the reciprocal of this value.

\(T = \dfrac{1}{3.33 \times 10^8} \approx 3.0 \text{ ns}\)