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

Step 1: Compute the total number of clock cycles \[ {Total cycles} = (2 \times 2.25 \times 10^8) + (5 \times 1.20 \times 10^8) + (4 \times 1.65 \times 10^8) + (3 \times 1.30 \times 10^8) \] \[ = 4.5 \times 10^8 + 6.0 \times 10^8 + 6.6 \times 10^8 + 3.9 \times 10^8 = 21.0 \times 10^8 \] Step 2: Compute the clock cycle time Clock rate \( f \) is given by: \[ f = \frac{{Total cycles}}{{Execution time}} \] \[ = \frac{2.10 \times 10^9}{6.3} = 3.33 \times 10^8 { cycles per second} \] Clock cycle time \( T \) is: \[ T = \frac{1}{f} = \frac{1}{3.33 \times 10^8} \approx 3.0 { nanoseconds} \]