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# Computer Organization and Design Transistors &amp; Logic - I

Computer Organization and Design Transistors &amp; Logic - I. Montek Singh Wed, Oct 10, 2012 Lecture 10. Today ’ s Topics. Why go digital? E ncoding bits using voltages D igital design primitives transistors and gates. Where are we in this course?. Things we know so far:

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## Computer Organization and Design Transistors &amp; Logic - I

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1. Computer Organization and DesignTransistors & Logic - I Montek Singh Wed, Oct 10, 2012 Lecture 10

2. Today’s Topics • Why go digital? • Encoding bits using voltages • Digital design primitives • transistors and gates

3. Where are we in this course? • Things we know so far: • Computers process information • Information is measured in bits • Data can be represented as groups of bits • Computer instructions are encoded as bits • We, humans, don’t want to deal with bits… • so we invent Assembly Language and Compilers • But, what PROCESSES all these bits?

4. A Substrate for Computation • We can build devices for processing and representing bits using almost any physical phenomenon • currents • voltages • tiny magnets (nanomagnets) • quantum phenomena (quantum computing) • sequences of DNA (DNA computing) • … • any physical phenomenon with at least 2 distinct states, which can be measured and controlled

5. Using Electromagnetic Phenomena • Things like: • voltages , phase, currents, frequency • Using voltages to encode information • Voltage pros: • easy generation, detection • voltage changes can be very fast • lots of engineering knowledge already • Voltage cons: • easily affected by environment • need wires everywhere to transmit

6. Encoding using Voltage (example) • Representation of each point (x, y) on a B&W pic: • 0 volts: BLACK • 1 volt: WHITE • 0.37 volts: 37% Gray, etc. • Representation of a picture: • scan points in some prescribedraster order… • generate voltage waveform How much information at each point?

7. Information Processing = Computation Copy v v INV v 1-v • First, let’s introduce some processing blocks:(say, using a fancy photocopier/scanner/printer)

8. Let’s build a system! (Reality) Copy INV Copy INV input Copy INV (In Theory) Copy INV ? output

9. Why Did Our System Fail? • Why doesn’t reality match theory? • COPY Operator doesn’t work right? • INVERSION Operator doesn’t work right? • Theory is imperfect? • Reality is imperfect? • Our system architecture stinks? • ANSWER: all of the above! • Noise and inaccuracy are inevitable • We cannotreliably reproduce infiniteinformation in the presence of noise • consequence of Shannon’s theorem • Must design our system to tolerate some amount of error if it is to process information reliably!

10. The Key to System Design • A SYSTEM is a structure that is guaranteed to exhibit a specified behavior, assuming all of its components obey their specified behaviors. • How is this achieved? CONTRACTS! • Every system component will have clear obligations and responsibilities. If these are maintained we have every right to expect the system to behave as planned. If contracts are violated all bets are off. • Much like object-oriented programming!

11. Let’s go digital! • Why DIGITAL? • … because it keeps the contracts SIMPLE! • The price we pay for this robustness? • All the information that we transfer between components is only 1 crummy bit! • But, in exchange, we get a guarantee of a reliable system. 0 or 1

12. The Digital Abstraction 0/1 Noise “Ideal”Abstract World RealWorld ManufacturingVariations Bits Volts or Electrons or Ergs or Gallons Keep in mind, the world is not digital, we engineer it to behave so.We must use real physical phenomena to implement digital designs!

13. Types of Digital Components • Two categories of components • those whose output only depends on their current inputs • called COMBINATIONAL • they are “memory-less”, don’t remember the past • those who output depends also on their past state • called SEQUENTIAL • they are “state-holding”, remember their past • key to building memories

14. Terminology • System • a reasonably large assembly of components • division of a system into components is typically arbitrary but almost always hierarchical • Component/Element • an individual part of a bigger system • clearly-defined function and interface • implement it and put a black-box around it • larger components created using smaller components • Circuit • a small (often leaf-level) component consisting of a network of gates

15. Combinational Components input A input B output Y input C • A circuit is combinational if-and-only-if it has: • one or more digital inputs • one or more digital outputs • a functional specification that details the value of each output for every possible combination of valid input values • output depends only on the latest inputs • a timing specification consisting (at minimum) of an upper bound tpd on the time this circuit will take to produce the output value once stable valid input values are applied Output a “1” if at least 2 out of 3 of my inputs are a “1”. Otherwise, output “0”. I will generate a valid output in no more than 2 minutes after seeing valid inputs

16. A Combinational Digital System • Theorem: A system of interconnected elements is combinational if-and-only-if: • each primitive circuit element is combinational • every input is connected to exactly one output or directly to a source of 0’s or 1’s • the circuit contains no directed cycles • no feedback (yet!) • Proof: By induction • Start with the rightmost level of elements • their output only depends on their inputs, which in turn are outputs of the level of element just to their left • and so on… until you arrive at the leftmost inputs • But, in order to realize digital processingelements we have one more requirement!

17. Noise Margins Valid “0” Valid “1” Forbidden Zone volts Invalid Min Voltage Max Voltage • Key idea: Keep “0”s distinct from the “1”s • say, “0” is represented by min voltage (e.g., 0 volts) • … “1” is represented by high voltage (e.g., 1.8 volts) • use the same voltage representation throughout the entire system! • For reliability, outlaw “close calls” • forbid a range of voltages between “0” and “1” CONSEQUENCE: Notion of “VALID” and “INVALID” logic levels

18. Digital Processing Elements I will only output a ‘1’ if an odd number of my inputs are ‘1’ I will only outputa ‘1’ if all my inputs are ‘1’ I will copy andrestore my inputto my output I will output thecomplement of my input I will output a ‘1’ if any of my inputs are ‘1’ AND XOR OR • Some digital processing elements occur so frequently that we give them special names and symbols A Y A Y buffer inverter A A Y Y B B A Y B

19. Digital Processing Elements AND XOR OR • Some digital processing elements occur so frequently that we give them special names and symbols A Y A Y buffer inverter A A Y Y B B A Y B

20. From What Do We Make Digital Devices? • Recall our common thread from Lecture 2… • A controllable switch is a common link of all computing technologies • How do you control voltages with a switch? • By creating and opening paths between higher and lower potentials (voltages) This symbol indicates a “high” potential, or the voltage of the power supply (e.g., 2V, 5V etc.) Load This symbol indicates a “low” or ground potential or 0V.

21. Most common technology today • … is called CMOS • everything built using transistors • a transistor is just a switch • 2 types of transistors • n-type • called “NFET”, or “nMOS” or “n channel transistor” or “n transistor” • switch is on (i.e., conducts) when its control input is ‘1’ • p-type • called “PFET”, or “pMOS”, or “p channel transistor” or “p transistor” • switch is on (i.e., conducts) when its control input is ‘0’ • need both types to build useful gates

22. N-Channel Field-Effect Transistors (NFETs) S D “ “ S D S D When the gate voltage is high, the switch connects. Good at pulling things “low”. + D D G G VDS³ 0 + S S VGS - Operating regions: cut-off: VGS < VTH linear: VGS³ VTH VDS < VDsat saturation: VGS³ VTH VDS³ VDsat - 0.5V IDS linear saturation VGS VGS - VTH VDS

23. P-Channel Field-Effect Transistors (PFETs) S D “ “ S D S D When the gate voltage is low, the switch connects. Good at pulling things “high”. S - S VGS - + G G VDS 0 + D D Operating regions: cut-off: VGS > VTH linear: VGSVTH VDS > VDsat saturation: VGSVTH VDSVDsat –0.5V -VDS -VGS VGS - VTH saturation linear -IDS

24. Next time • Build gates using transistors • Build larger circuits using gates

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