Category: Computer Architecture

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2 ^ 10 = 1024

2 ^ 10 = 1 KB of memory

2 ^ 20 = 1 MB of memory

2 ^ 30 = 1 GB of memory

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$10^{-12}$	pico
$10^{-9}$	nano
$10^{-6}$	micro
$10^{-3}$	milli
$10^{3}$	Kilo
$10^{6}$	Mega
$10^{9}$	Giga
$10^{12}$	Tera

Performance

Response Time: Time taken to do a particular task

Throughput: Total workdone per unit time

$$Performance = \frac{1}{\text{Execution Time or Response Time}}$$

$$\frac{Performance_{x}}{Performance_{y}} = \frac{Execution_{y}}{Execution_{x}}$$

Clock Period: Duration of a clock cycle. e.g., 250 ps (picosecond)

Clock frequency: Number of clock cycles per second. e.g., 40 GHz or $40\times{10}^{9}\frac{cycles}{second}$

$$\text{Program CPU Time} = \text{# of CPU Clock Cycles}\times\text{Clock Cycle Time or Clock Period} = \frac{\text{CPU Clock Cycles}}{\text{Clock Rate}}$$

However,

$$\text{CPU Clock Cycles}=\text{Instruction count of a program(IC)}\times\text{# of cycles per instruction(CPI)}$$

Therefore,

$$\text{Program CPU Time}=\frac{IC\times{CPI}}{\text{Clock Rate}}$$

Weighted Average CPI:

$$CPI_(\text{weighted avg})=\frac{\sum_{i}^{}IC_i\times{CPI_i}}{\text{Total Instruction Count}}$$

MIPS(Million Instructions Per Second):

$$MIPS=\frac{\text{Instruction Count}}{\text{CPU Time}\times{10}^6}$$

Substituting CPU Time in the above equation,

$$MIPS=\frac{\text{Clock Rate}}{\text{CPI}\times{10}^6}$$