Suppose that you design an architecture with the following characteristics

Cost of a non?branch instruction 1 cycle
Fraction of instructions that are branches 20%
Fraction of branches that are taken 85%
Fraction of delay slots that can be filled 50%
Cost of an unfilled delay slot 1 cycle

For this architecture
a. calculate the average number of cycles per instruction
b. calculate the improvement (as a percentage) if the fraction of delay slots that are filled can be increased to
95%.

a. Average cycles = non?branch cycles + non?taken branches + taken branches slot filled + taken branches slot
unfilled.
= 80% × 1 + 20%(15% × 1 + 85% × (50% × 1 + 50% × 2))
=0.80 + 0.20 × (0.15 + 0.85 × (0.50 + 1.00) = 0.80 + 0.20 × (0.15 + 1.275) = 1.085
b. The only thing different is the fraction of unfilled slots. We can write
Average cycles = 80% × 1 + 20%(15% × 1 + 85% × (95% × 1 + 5% × 2))
= 0.80 + 0.20(0.15 + 0.8925) = 1.0085.