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
Low level components Not Symbol that implies the inverse Add a circle before a connection on a diagram…
Low level components Transistor Critical piece of technology Faucet analogy Not gate
Low level components Gates Not Bill Graphical representation of groups of transistors And gate (Just like && in programming)
Low level components Or / Not Symbols Or NorXor Xnor
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
Low level components Math DeMorgans Theorem Not (P and Q) = (Not P) or (Not Q) Not (P or Q) = (Not P) and (Not Q)
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
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
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)
Low level components Process Transformation Using DeMorgans Law: A or B => Not ( Not (A + B) ) Not ( Not (A and B) )
Low level components Tedious Not difficult, just requires patience and practice Practice –Turn an AND gate into NAND gates ???
Low level components Answer Note: We need to invert the answer So and it with itself and invert it again
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?
Low level components Summary Transistors Wires Gates Math Example of why we learn about them