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ITEC 352 Lecture 2 Low level components

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Review Electricity Math Components

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Low level components Foundatio n Wires –Why are they coated with rubber? –Crossing wires are not connected –Terminated are –Curved bump is not connected –Represented as

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Low level components Not Symbol that implies the inverse Add a circle before a connection on a diagram…

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Low level components Transistor Critical piece of technology Faucet analogy Not gate

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Low level components Gates Not Bill Graphical representation of groups of transistors And gate (Just like && in programming)

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Low level components Or / Not Symbols Or NorXor Xnor

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Low level components Hardware Not all hardware is constructed equally Some is easier than others Can construct all logic using limited set of gates (and/or/not, NAND) NAND gates –Easiest / cheapest to produce Problem –We dont naturally think in NAND gates

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Low level components Math DeMorgans Theorem Not (P and Q) = (Not P) or (Not Q) Not (P or Q) = (Not P) and (Not Q)

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Low level components Idempotenc e Fancy word, simple concept And a value, what do you get? Or a value what do you get? Useful for translating one gate type to another

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Low level components Others Distributive Associative A and (B or C) = (A and B) or (A and C) A or (B and C) = (A or B) and (A or C) A and (B and C) = (A and B) and C A or (B or C) = (A or B) or C

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Low level components Others Absorption Consensus A and ( A or B) = A A or (A and B) = A (A and B) Or (Not A and C) Or (B and C) = (A and B) Or (Not A and C) (A or B) and (Not A or C) and (B or C) = (A or B) and (Not A or C)

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Low level components Process Transformation Using DeMorgans Law: A or B => Not ( Not (A + B) ) Not ( Not (A and B) )

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Low level components Tedious Not difficult, just requires patience and practice Practice –Turn an AND gate into NAND gates ???

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Low level components Answer Note: We need to invert the answer So and it with itself and invert it again

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Low level components Why? Adding binary numbers What all do we have to consider for adding 2 numbers together? How do we represent this using gates?

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Low level components Summary Transistors Wires Gates Math Example of why we learn about them

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