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)

To find the clock cycle duration, we calculate the total number of clock cycles required to execute all the instructions:

1. Clock cycles per instruction type:

   • Branch: $2.25 \times 10^8 \times 2 = 4.50 \times 10^8$ cycles

   • Load: $1.20 \times 10^8 \times 5 = 6.00 \times 10^8$ cycles

   • Store: $1.65 \times 10^8 \times 4 = 6.60 \times 10^8$ cycles

   • Arithmetic: $1.30 \times 10^8 \times 3 = 3.90 \times 10^8$ cycles

2. Total clock cycles:

   $$\text{Total Cycles} = (4.50 + 6.00 + 6.60 + 3.90) \times 10^8 = 21.0 \times 10^8\text{ cycles}$$

3. Clock cycle duration ($T_{\text{clk}}$):

   $$\text{Execution Time} = \text{Total Cycles} \times T_{\text{clk}}$$

   $$6.3\text{ s} = 21.0 \times 10^8 \times T_{\text{clk}}$$

   $$T_{\text{clk}} = \frac{6.3}{21.0 \times 10^8} = 0.3 \times 10^{-8}\text{ s} = 3.0 \times 10^{-9}\text{ s} = 3.0\text{ ns}$$

Thus, the duration of a clock cycle is 3.0 nanoseconds.