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. Typed/computer printed assigments not accepted. Include units of measurement in the conversion.

Base 10 - Clock speeds

Ex. 1 MHz = 1 * 10^6 cycles/sec.
One clock cycle is 1 / ( 1 * 10^6 cycles/sec. ) or 1/1 * 1 * 10^-6 sec/cycle.
or 1 uSec/cycle

1 Hz = 1 cycle/sec. 1 Hz = 1 Hertz 1 GHz GigaHertz 10^9 1 MHz MegaHertz 10^6 1 KHz KiloHertz 10^3

1 ps picosecond 10^-12 sec. 1 ns nanosecond 10^-9 sec. 1 us microsecond 10^-6 sec.,   use u or mu. 1 ms millisecond 10^-3 sec. 1 second = 10^9 nsec/sec.

Use 6 digits precision for answers.

1. Given the following clock speeds, give the time of a single clock cycle. A.   25 MHzin microseconds B.   8 MHzin microseconds C.   500 MHzin nanoseconds D.   2 GHzin nanoseconds E.   4 KHzin milliseconds

2. Given the following time for a single clock cycle, give the speed of the clock in cycles/sec.

A.   1 ns

B.   8 microsecond(usec)

C.   25 microsecond

D.   40 psec.

3.,4.,5. Pipelines and Parallel architecture.

Example : 1 cycle/sec. * 1 inst./cycle = 1 inst./sec.
1 inst./sec. * 1 sec/cycle. = 1 inst./cycle.

Instruction takes 1 uS to complete : If 1 inst. / 10-6 sec., then
1 inst./usec. * 10^6 usec./sec. = 10^6 inst./sec.

Given a datapath with a fetch (fi), decode (de), fetch operand (fo) execute(ex), and a writeback(wb) stage.

Assume 1 ns per cycle (clock). Carry the number out to 6 significant digits if needed.

This table presents 3 instruction types with their timing signiture for each step of a fetch/execute pipeline.

4 clocks  

Type	Fetch opcode	Decode	Fetch operands	Execute	Write back
A	1 clock	1 clocks	1 clocks	1 clocks	1 clock
B	1 clock	1 clocks	10 clocks	4 clock
C	1 clock	1 clock	4 clocks	4 clock	0 clock

For each instruction type, find the following. Work all parts for one type at a time.

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

B. If pipelining not supported, calcualte number of instructions per second.

C. If pipeline supported and full, how often is an instruction completed.

D. Calculate number of instructions per second.

E. If the execution step is paralleled, calculate the number of instructions per second.

6. Base 2 Memory blocks.

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

A. How many 128k blocks are in 16 Meg of memory?

B. How many 32 byte blocks are in 1 Meg of memory?

C. How many 64K blocks are in 4 Gig of memory?

D. How many 16 byte blocks are in 64 Meg of memory?

E. If address bus is 32 bit, what is full memory range?

F. If address bus is 36 bit, what is full memory range?

G. If address bus is 44 bit, what is full memory range?