Architecture Computations

• Generally we are interested in questions involving computer speed.
  • What are the units of speed in a computer?
• We will look at different ways you could possibly build a computer.
• We will want to be able to discuss performance of different options so we can compare.
• To do this, we must define what performance is.
  • We will discuss performance in some detail later, but for now we will define it to be time spent on a program.
• The basic components of time in a program.
  • The clock
  • The number of instructions in the program.
  • The number of cycles per instruction (CPI)
• The clock
  • Discussed on page 33 of the book.
  • Discussed in appendix B.7
  • This is the driver of the CPU
  • It is an electronic signal that changes between a low signal and a high signal.
  • This could be a sin/cos wave, or probably a shaped.
• A clock cycle
  • Is one iteration of the clock.
  • It generally has a rising edge, where most logic takes place.
  • But we can shape the clock if we wish, more on that later.
  • (From alanclements.org)
• The clock frequency is the amount of cycles run in a given time period.
  • Normally this is cycles per second.
  • The unit for this is Hertz (Hz).
  • A 1 Hz Clock has a frequency of one cycle per second.
  • $\frac{\text{cycles}}{\text{second}}$
  • What are typical clock rates?
• Clock cycle time
  • This is $\frac{\text{seconds}}{\text{cycle}}$
  • My windows machine claims to run at 2.6GHz, how long is each cycle?
    • $2.6GHz = \frac{2.6\times10^{9}\text{cycles}}{1\text{second}}$.
    • That is the same as $\frac{1\text{second}}{2.6\times10^{9}\text{cycles}}$
    • Or $\frac{1}{2.6} \times 10^{-9} \frac{\text{seconds}}{\text{cycle}}$
    • or $0.38 \times 10^{-9} \frac{\text{seconds}}{\text{cycle}}$
    • So a cycle is $0.38 \times 10^{-9} \text{seconds}$.
    • So a cycle is $3.8 \times 10^{-10} \text{seconds}$.
    • This doesn't seem like a good answer, let's change units.
    • What unit do I want? (nano seconds or pico seconds?) (pico)
    • $ 1 \text{second} = 1 \times 10^{12} \text{pico seconds}$
    • $3.8 \times 10^{-10} \text{seconds} \times \frac{1 \times 10^{12} \text{pico seconds}}{1 \text{seconds}}$
    • $3.8 \times 10^{\cancel{-10} 1} \cancel{\text{seconds}} \times \frac{1 \times 10^{\cancel{12} 2} \text{pico seconds}}{1 \cancel{\text{seconds}}}$ That 12 should be canceled
    • Or $3.8 \times 10^2$ps
    • Or 380 ps/cycle.
  • Why is this important?
    • this is, in theory, how long it will take to execute a single instruction!
• The number of instructions per program.
  • These are machine/assembly instructions.
  • We will be able to tell the difference later, but for now you can think of them as semi-equivalent.
  • Right now we will consider all instructions of equal weight.
  • We will discover that this is not the case later.
  • We will discuss this in more detail later.
• The final part of the mix is CPI or IPC .
  • Cycles per instruction.
  • Ideally we would like to be able to execute an instruction every cycle.
  • But we might not be able to do this.