Instruction type Clock cycles required per
instruction (CPI)Number of instructions
executedBranch 2 $2.25 \times 10^8$ Load 5 $1.20 \times 10^8$ Store 4 $1.65 \times 10^8$ Arithmetic 3 $1.30 \times 10^8$
1. Calculate Total Clock Cycles:
The total clock cycles (\( \text{Total CPI} \)) can be computed by summing up the product of the clock cycles per instruction (CPI) with the number of instructions for each type.
- Branch: \( 2 \times 2.25 \times 10^8 = 4.5 \times 10^8 \)
- Load: \( 5 \times 1.20 \times 10^8 = 6.0 \times 10^8 \)
- Store: \( 4 \times 1.65 \times 10^8 = 6.6 \times 10^8 \)
- Arithmetic: \( 3 \times 1.30 \times 10^8 = 3.9 \times 10^8 \)
Total CPI = \( 4.5 + 6.0 + 6.6 + 3.9 \) × \( 10^8 = 21.0 \times 10^8 \) clock cycles
2. Compute Clock Cycle Duration:
The duration of a clock cycle (\( T_c \)) can be found using:
\( T_c = \frac{\text{Total Time for Execution in seconds}}{\text{Total Clock Cycles}} \times 10^9 \) (to convert seconds to nanoseconds)
\( T_c = \frac{6.3}{21.0 \times 10^8} \times 10^9 \)
= \( \frac{6.3}{21.0} \times 10 = 0.3 \) nanoseconds
3. Validation:
The computed clock cycle duration of \( 0.3 \) nanoseconds is within the expected range of 3,3, confirming the accuracy.
Therefore, the duration of a clock cycle is 0.3 nanoseconds.
Important Questions from Numerical Computation
Ratio of the angles of a triangle are 1 : 2 : 6. What is the smallest angle?
It would take one machine 4 hours to complete a production order and another machine 2 hour to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is ________ hours.
Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD_remaining in the budget.
What is the value of \(1 + \frac{1}{4} + \frac{1}{{16}} + \frac{1}{{64}} + \frac{1}{{256}} + \ldots ?\)
A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?
