A CPU accesses 100 program instructions. Each memory access takes 5 ns. The memory can only hold 50 instructions. The first 50 instructions are already in memory. Replacing those 50 by the next 50 takes 400 ns. What is the total time in ns?

1 answer

To calculate the total time taken for the CPU to access the 100 program instructions, we need to consider both the memory accesses and the instruction replacements.

Initial 50 Instructions:

The first 50 instructions are already in memory, so accessing these will take:

\[ \text{Time for first 50 instructions} = 50 \text{ instructions} \times 5 \text{ ns/instruction} = 250 \text{ ns} \]

Next 50 Instructions:

After accessing the first 50 instructions, the CPU needs to access the next 50 instructions. Since the memory can only hold 50 instructions at a time, it must first replace the currently held instructions. This replacement takes 400 ns.

After the replacement, the CPU can access the next 50 instructions, which takes another 250 ns:

\[ \text{Time for replacing instructions} = 400 \text{ ns} \] \[ \text{Time for the next 50 instructions} = 50 \text{ instructions} \times 5 \text{ ns/instruction} = 250 \text{ ns} \]

Total Time Calculation

Now, we sum all the time components together:

\[ \text{Total Time} = \text{Time for first 50 instructions} + \text{Time for replacing instructions} + \text{Time for next 50 instructions} \] \[ \text{Total Time} = 250 \text{ ns} + 400 \text{ ns} + 250 \text{ ns} = 900 \text{ ns} \]

Thus, the total time taken for the CPU to access all 100 program instructions is:

\[ \boxed{900 \text{ ns}} \]

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