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Engin112-F07-L15-combinational

# Engin112-F07-L15-combinational - Engin112 Lecture 15...

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Maciej Ciesielski Department of Electrical and Computer Engineering 10/09/2007 Engin112 – Lecture 15 Combinational Circuits 10/09/2007 Engin 112 - Intro to ECE 2 Recap from last lecture Incompletely specified functions y Don’t cares in Karnaugh map NAND and NOR implementations y NOT, AND, OR from NAND or OR gates y Convert sum of terms into NAND implementation » AND-invert and invert-OR representation » “Double bubbles” This lecture y Combinatorial circuits » Analysis of circuits » Design of circuits

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10/09/2007 Engin 112 - Intro to ECE 3 Conversion Example Contest: implement function F(A,B,C,D) = (0,2,7,8,10,13) d(A,B,C,D) = (6,14,15) y Group 1 : K-map, minimize function, NAND implementation y Group 2: K-map, minimize function, NOR implementation Solution (SOP form): F = BC + B’D’ + ABD NAND NOR F = [ ( BC + B’D’ + ABD )’ ] = [ (BC) (B’D’) (ABD) ] NANDs NAND F = { [ (BC)’’ + (B’D’)’’ + (ABD)’’ ]’ }’ = { [ (B’+C’)’ + (B+D)’ + (A’+B’+D’)’ ]’ }’ inverter NORs NOR 10/09/2007 Engin 112 - Intro to ECE 4 Combinational Circuits So far: single function with one output y Most realistic problems use multiple outputs Need to extend to combinational circuits : y Combinational circuits » Outputs depend on the inputs (only) Important distinction: combinational vs sequential circuits y Sequential circuits (next chapter) » Outputs depend on inputs and previous state (outputs) »
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