Lecture 02

Class: CSE 120 Subject: computer-science computer-architecture Date: 2025-04-07 Teacher: **Prof. Nath

Transistors

Denard Scaling

• Denard Scaling is a way to scale transistor parameters(including voltage) to keep power density constant

A question to ask is, if transistor size has kept decreasing (250nm in 1997 to 2nm in 2025), why has frequency started flatlining?

End of Denard Scaling

• a huge drawback to Denard Scaling is that it ignored the “leakage current” and “threshold voltage” which establish a baseline of power per transistor.
• as a result, it has created a “power wall” that has limited processor frequency to around 4GHz since 2006(yikes!)

Potential Improvements

1. Using multiple cores
2. Parallelism
3. Speculative prediction

Performance

Latency

• latency is the interval between stimulation and response(basically how long it takes to do a task)

Base Units

Clock Period

• clock period refers to the duration of a clock cycle
  • i.e. $250ps=0.25ns=250\ast 10^{-12}s$
  • this is the basic unit of time in all computers

Clock Frequency/Rate/Speed

• clock frequency/clock rate/clock speed is cycles per second
  • i.e. $4.0GHz=4000MHz=4.0\ast 10^{9}Hz$

Execution Time

• Execution Time = Cycles Per Program * Clock Cycle Time
• which is also the same as = Cycles Per Program / Clock Frequency/Rate/Speed

Ways to Increase Execution Time

1. Reduce the Cycles Per Program
2. Increase the Clock Frequency

Bandwidth

• bandwidth is also known as throughput
• bandwidth refers to how much of $X$ work is done in a given time.

Speed Up

• performance overall improved execution for a whole problem

• for future reference, use (times or x)
  • i.e. 2.1x speed up

is throughput the inverse of latency? yes if the tasks are done one after the other no if the tasks are done in parallel

Little’s Law

• Little’s Law refers to the average number of transactions in a stable system is equal to their average arrival rate, multiplied by their average time in the system.

Parallelism

• parallelism is equal to throughput(bandwidth) * latency

Amdahl’s Law

• refers to the maximum possible speed up achievable by optimizing a part of a system

$=\frac{1}{\frac{F_{parallel}}{n}+(1-F_{parallel})}$

• $F_{parallel}$ = fraction of time improved
• $n$ = how much faster that part gets

Example

• What is the overall speedup if half of the execution sped up by 2x?

$F_{parallel}$ = 0.5 $n$ = 2

$=\frac{1}{\frac{0.5}{2}+(1-0.5)}$