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# lec11 - ENGR 111 Lecture 11 Reading Chapters 22 Class notes...

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ENGR 111 Lecture 11 Reading: Chapters 22 Class notes

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Review of last lecture z Binary representation, binary addition z Gates - Inverter, AND, OR, NAND, NOR, XOR, XNOR z Logic implementation of 1-bit half adder
General Technique for Logic F = ABC + ABC +ABC+ ABC

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General Technique for Logic …
Binary Addition Truth Table A i B i C in C out S i 00000 00101 01001 01110 10001 10110 11010 11111

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Logic for Full Binary Addition + ++ ii i in n i i in i i n out i in i in in iii n S=ABC ABC C= A B C + A B +AB C + ABC C
Logic Rules – AND () AA = A A0 = 0 A1 = A = 0 AB = BA C A BC + C = A B + A C ⋅⋅ ⋅=⋅

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Logic Rules – OR () ( ) = A+0=A A+1=1 A+A=A A+B=B+A A+A=1 A+ B+C A+B +C A+BC= A+B A+C ( ) =A+BA+AC+BC=A 1+B +AC+BC =A+AC+BC=A 1+C +BC=A+BC
Logic Rules z The logic rules allow simplification of logic or logic minimization { Reduces the number of inputs, gates needed to generate the same output

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DeMorgan’s Laws z Relate AND and OR implementations { AND can be converted into NOR of inverted inputs { OR can be converted into NAND of inverted inputs A B=A+B A+B=A B
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lec11 - ENGR 111 Lecture 11 Reading Chapters 22 Class notes...

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