The following are a series of math problems common to computer systems. Work out each problem. Do the work on a separate piece of paper with a pencil and show your work (include units of measurement. Typed copies are not acceptable.

Base 10 - Clock speeds

MHz MegaHertz (cycles/sec) 10^6
KHz KiloHertz  10^3
ns  nano-second 10^-9
ms  millisecond 10^-3
For microsecond, use the mu symbol.

Use 6 digits precision for answers.

Given the following clock speeds, give the time in nanoseconds of a
single clock cycle.

1. 4.7 MHz         2.  100 MHz          3.   25 MHz

4.  2.1 GHz        5.   32 MHz


Given the following clock speeds, give the time in microseconds of a
single clock cycle.

6. 9600 cycles/sec    7. 33.3 KHz     8. 56,000 cycles/sec


Given the following time for a single clock cycle, give the speed of the
clock.

9.  10 ns           10.  4 microsecond      11.  25 microsecond

12. 12 ns

Given a pipeline with a fetch (fi), decode (de), operand fetch (fo), execute(ex), and a writeback(wb) stage. The timing for each step is given for each problem. Assume 1 ns per cycle. Carry the number out to 4 significant digits.

Timing for type A instructions.

fi = 1ns, de = 2ns, fo = 3ns, ex = 8ns, wb = 1ns

13. Give the time it takes to process one instruction.

14. If the pipeline is full, how often is an instruction completed.

15. What is the number of instructions per second.

Timing for type B instructions.

fi = 1ns, de = 2ns, fo = 1ns, ex = 15ns, wb = 1ns

16. Give the time it takes to process one instruction.

17. If the pipeline is full, how often is an instruction completed.

18. What is the number of instructions per second.

Timing for type C instructions.

fi = 1ns, de = 1ns, fo = 0ns, ex = 1ns, wb = 1ns

19. Give the time it takes to process one instruction.

20. If the pipeline is full, how often is an instruction completed.

21. What is the number of instructions per second.

22. If a system is pipelined and performs 85% of type A instructions and 15% of type B instructions, what is the average MIPS for the system?

23. If a system is pipelined and performs 60% of type A instructions and 15% of type B instructions and 25% of type C instructions, what is the average MIPS for the system?

For the types of instructions listed above, assume that the pipeline is super-scalar at the execution stage (dual execution stage), give the MIPS for each. Assume no conflicts.

24. Type A           25. Type B            26. Type C

27. If a system is super-scalar and performs 85% of type A instructions and 15% of type B instructions, what is the average MIPS for the system?

28. If a system is super-scalar and performs 60% of type A instructions and 15% of type B instructions and 25% of type C instructions, what is the average MIPS for the system?

Base 2  Memory blocks.

   16 = 2^4
  256 = 2^8
 1024 = 2^10
65536 = 64K = 2^16
 1Meg = 2^20
 1Gig = 2^30

29. How many 64K blocks are in 16 Meg of memory?

30. How many 16 byte blocks are in 1 Meg of memory?

31. How many 4K blocks are in 1 Gig of memory?

32. How many 32 byte blocks are in 64 Meg of memory?