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U of I CS 231 - Administrative Matters

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CS231: Computer Architecture ILuddy HarrisonSpring 2006Introduction to CS2311Administrative Matters• The course web site will go online by the end of the day on Thursday, Jan 19– Office hours, policies, schedule, etc. will be posted– A tentative set of lecture notes – from previous semesters – will be posted• The notes for each class will be updated prior to the class– I will sometimes modify the notes right up to the minute the class begins• Sorry– Therefore you should download the class notes after a lecture– As far as possible, I will simply insert additional slides; if you print out the notes prior to class you will usually be able to print out just the additional slides• Please feel free to email me! I like email.– [email protected] to CS2312Course Objectives• To learn how to design digital (i.e. boolean)circuits • To Understand how a simple computer works– Its hardware components – What they are built from– How to design them– Also, how to design digital circuits other than computers• Today– A grand overview– How have we been able to make a “Machine” that can do complex things• Add and multiply reallyfast • Weather forecast, design of medicinal drugs• Speech recognition, Robotics, Artificial Intelligence..• Web browsers, internet communication protocols• Starting at (almost) the lowest level– Gates to GatesIntroduction to CS2313The Modest Switch• All these capabilities are built from an extremely simple component:– A controllable switch• The usual Electrical switch we use every day– The electric switch we use turns current on and off– But we need to turn it on and off by hand– The result of turning the switch on?• The “top end” in the figure becomes• raised to a high voltage• Which makes the current flow through the bulb•The Controllable Switch•No hands•Voltage controls if the switch is on or off•High voltage at input: switch on •Otherwise it is offIntroduction to CS2314Using the switchOutputInput Output is high (voltage) if and only if the input is highNow we can make one circuit control another switch…Neat!This is getting boring..Introduction to CS2315Lets use them creativelyOutput is high if both the inputs input1 ANDinput2 are highIf either of the inputs is low, the output is low.Input1Input2OutputThis is called an AND gateNow, can you make an OR gate with switches?Introduction to CS2316OR GateInput1Input2OutputOutput is low iff both inputs are lowI.e. Output is high if either of the inputs (or both) are high (input1 OR input2)Introduction to CS2317Basic Gates • There are three basic kinds of logic gatesANDof two inputsOR of two inputsNOT(complement)on one inputOperation:Logic gate:•Two Questions:•How can we implement such switches?•What can we build with Gates? And How?Introduction to CS2318How to make switches?• Use mechanical power• Use hydrolic pressure• Use electromechanical switches (electromagnet turns the switch on)• Current technology:– Semiconductor transistors• A transitor can be made to conduct electricity depending on the input on the 3rdinput– CMOS “gates” (actually, switches)• We can now manufacture millions of transistors on a single silicon chip!Two properties of Switches and Gates:SizeSwitching and Propagation delaySo, switches and Gates are no magic.We believe they can be builtIntroduction to CS2319A little bit about technology• Two properties of Switches and Gates:– Size– Switching and propagation delay• Smaller the size, smaller the propagation delay (typically)!• Smaller the size, cheaper the processor!– Silicon is sand anyway– But you can put more logic on a single chip• This nice positive feedback cycle has– Made processors faster and cheaper– Over the last 30 years! (1972: Intel 4004)• Before that: A processor was built with MANY chipsIntroduction to CS23110What can we do with Gates?• What do you want to do?• Let us say we want to add numbers automatically• What are numbers? How are they represented– Roman XVII– Decimal: 17• How to add them, depends on how they are represented– One representation may be better than other for adding• Try adding two long roman numbers– Decimal is better but• We have only two “values”, high and low, in our gates– So, • Let us think about why decimal is better• And can we design a representation that allows us to use the binary (hi/low) gates that we have.Introduction to CS23111Decimal review• Numbers consist of a bunch of digits, each with a weight• These weights are all powers of the base, which is 10. We can rewrite this:• To find the decimal value of a number, multiply each digit by its weight and sum the products. 1 62.375Digits100 10 1 1/10 1/100 1/1000 Weights1 62.375Digits10210110010-110-210-3Weights(1 x 102) + (6 x 101) + (2 x 100) + (3 x 10-1) + (7 x 10-2) + (5 x 10-3) = 162.375Now we can see why addition is easier with decimal system than the roman system. The idea of positional weightsand carry!Introduction to CS23112Nothing special about 10!• Decimal system (and the idea of “0”) was invented in India around 100-500AD• Why did they use 10? Anything special about it?– Not really.– Probably the fact that we have 10 fingers influenced this• Will a base other than 10 work?– Sure: 345 in base 9 = 5 +9*4 + 92*3 = 284 in base 10• Base 9 has only 9 symbols: 1, 2, 3, 4, 5, 6, 7, 8, 0– What about base 2? (1 and 0)• 1101 in base 2: 1 + 2*0 + 4*1 + 8*1 = 13• Base 2 system will work for our gates!– Base 2 Addition:– Compare this with decimal addition100110111011001+Introduction to CS23113Converting binary to decimal• We can use the same trick to convert binary, or base 2, numbers to decimal. This time, the weights are powers of 2.– Example: 1101.01 in binary– The decimal value is:1101.01Binary digits, or bits232221202-12-2Weights (in base 10)(1 x 23) + (1 x 22) + (0 x 21) + (1 x 20) + (0 x 2-1) + (1 x 2-2) = 8 + 4 + 0 + 1 + 0 + 0.25 = 13.25Powers of 2: Useful abbreviations:20 = 1 24 = 16 28 = 256 K = 210 = 1,02421 = 2 25 = 32 29 = 512 M = 220 = 1,048,57622 = 4 26 = 64 210 = 1024 G = 230 = 1,073,741,82423 = 8 27 = 128Introduction to CS23114Binary addition example worked out• Some terms are given here• Exercise: what are these numbers equivalent to in decimal?1110 (Carries)1011(Augend)+ 1110(Addend)1 1 0 0 1 (Sum)The initial carryin is implicitly 0most significantbit


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U of I CS 231 - Administrative Matters

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