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

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

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

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

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

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

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

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

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

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. 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! Much like object-oriented programming! 10

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

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

13. Types of Digital Components  Two categories of components those whose output only depends on their current inputs 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 those who output depends also on their past state  called SEQUENTIAL  they are “state-holding”, remember their past  key to building memories 13

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

15. Combinational Components  A circuit is combinational if-and-only-if it has: one or more digital inputs one or more digital inputs one or more digital outputs one or more digital outputs a functional specification that details the value of each output for every possible combination of valid input values 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 t pd on the time this circuit will take to produce the output value once stable valid input values are applied a timing specification consisting (at minimum) of an upper bound t pd 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 input A input B input C output Y 15

16. A Combinational Digital System  Theorem: A system of interconnected elements is combinational if-and-only-if: each primitive circuit element is combinational 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 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 the circuit contains no directed cycles  no feedback (yet!)  Proof: By induction Start with the rightmost level of elements 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 processing elements we have one more requirement! 16

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

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

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

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 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) By creating and opening paths between higher and lower potentials (voltages) Load This symbol indicates a “low” or ground potential or 0V. This symbol indicates a “high” potential, or the voltage of the power supply (e.g., 2V, 5V etc.) 20

21. Most common technology today  … is called CMOS everything built using transistors everything built using transistors a transistor is just a switch a transistor is just a switch  2 types of transistors n-type 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 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 need both types to build useful gates 21

22. N-Channel Field-Effect Transistors (NFETs) D G S D G S + + - - V GS V DS  0 Operating regions: cut-off: V GS < V TH linear: V GS  V TH V DS < V Dsat saturation: V GS  V TH V DS  V Dsat SD V GS - V TH 0.5V SD SD ““ I DS V DS V GS linearsaturation When the gate voltage is high, the switch connects. Good at pulling things “low”. 22

23. P-Channel Field-Effect Transistors (PFETs) S G D S G D + - - + V GS V DS  0 Operating regions: cut-off: V GS > V TH linear: V GS  V TH V DS > V Dsat saturation: V GS  V TH V DS  V Dsat SD V GS - V TH –0.5V SD SD ““ -I DS -V DS -V GS linearsaturation When the gate voltage is low, the switch connects. Good at pulling things “high”. 23

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