Question

An instruction pipeline has five stages where each stage takes 2 nanoseconds and all instructions use all five stages. Branch instructions are not overlapped, i.e., the instruction after the branch is not fetched till the branch instruction is completed. Under ideal conditions.

(a) Calculate the average instruction execution time assuming that 20% of all instruction executed are branch instructions. Ignore the fact that some branch instructions may be conditional.
(b) If a branch instruction is a conditional branch instruction, the branch need not be taken. If the branch is not taken, the following instructions can be overlapped. When 80% of all branch instructions are conditional branch instructions, and 50% of the conditional branch instructions are such that the branch is taken, calculate the average instruction time.
a. 2.96 nano seconds
b. 3.6 nano seconds
c. Both A and B
d. None of the above

Answer 1

Under ideal conditions, part (a) calculates to an average instruction time of 5.6 ns, and part (b) calculates to 2.8 ns when taking conditional branches into account. None of the given options match these calculations; therefore, the correct answer is (d) None of the above.

Step-by-step explanation:

Calculating Average Instruction Execution Time

Part (a): Under ideal conditions with no overlap for branch instructions, for every 5 instructions, 1 is a branch (20% of instructions are branches), which adds an additional 10 ns delay since we must wait for the entire pipeline to clear before fetching the next instruction. Thus, the average time per instruction is as follows:

• 4 non-branch instructions take 2 ns each: 4 instruction * 2 ns = 8 ns.
• 1 branch instruction effectively takes 10*2 ns = 20 ns (for 5 stages at 2 ns each).
• Total time for 5 instructions = 8 ns (non-branch) + 20 ns (branch) = 28 ns.
• Average instruction time = 28 ns / 5 instructions = 5.6 ns.

However, the options provided do not include 5.6 ns, therefore none of the given answers match our calculation.

Part (b): Assuming 80% of branch instructions are conditional and only half of those take the branch, the calculation for average instruction time is adjusted:

• Out of 5 instructions, if 1 is a branch instruction, 80% of that is conditional, so 0.8 instructions allow pipelining. Of these, 50% do not take the branch, which is 0.4 instructions on average.
• The 0.4 instructions that do not take the branch allow for overlap, so no extra time is added.
• For the remaining 0.6 branch instructions (including the 0.4 that do take the branch), the penalty is still 10 ns each.
• Total time for 5 instructions = 8 ns (non-branch) + 10 ns * 0.6 (branch) = 8 ns + 6 ns = 14 ns.
• Average instruction time = 14 ns / 5 instructions = 2.8 ns.

Again, the options provided do not include 2.8 ns, so the answer is none of the above.