Consider a multi-level computer interpreting all levels where:
all Level 1 instructions are converted to 10 Level 0 instructions; all Level 2 instructions are converted to 8 Level 1 instructions; all Level 3 instructions are converted to 5 Level 2 instructions; all Level 4 instructions are converted to 5 Level 3 instructions; and all Level 5 instructions are converted to 5 Level 4 instructions.
If a Level 0 instruction takes 29.1 ns to fetch, decode, and execute, how many microseconds does it take to execute an instruction on Level 5?

Level 5 = 291 ms

Explanation:

Given Data:

Level 1 = 10 X Level 0 Instructions

Level 2 = 8 x Level 1 Instructions

Level 3 = 5 x Level 2 Instructions

Level 4 = 5 x Level 3 Instructions

Level 5 = 5 x Level 4 Instructions

Level 0 execution time = 29.1 ns

To Find:

Level 5 Execution Time = ?

Solution:

Put value of Level 1 in Equation of Level 2

Level 2 =  8 x 10 Level 0 = 80 x Level 0

Put value of Level 2 in Equation of Level 3

Level 3 = 5 x 80 x Level 0 = 400 x Level 0

Put value of Level 3 in Equation of Level 4

Level 4 = 5 x 400 x Level 0 = 2000 x Level 0

Put value of Level 4 in Equation of Level 5

Level 5 = 5 x 2000 x Level 0 = 10,000 x Level 0

So, Level 5 have total of 10,000 Level 0 Instruction. Each level 0 Instruction takes 29.1 ns time to execute. So, Level 5 will Take

Level 5 = 10,000 x 29.1 ns

            =  2,91,000 ns

Level 5 = 291 ms