218L7F08a - ESE218 Lecture 7. AOI and OAI implementations....

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9/23/08 ESE218 Fall 2008 Lecture 7 1 ESE218 Lecture 7. AOI and OAI implementations. Gate-level minimization. Glitch-free design Outline ± AOI implementation ± function complement in SOP form ± circuit diagrams ± OAI implementation ± function complement in POS form ± Logical adjacency ² algebraic expression ² graphical representation ± Logic minimization with K-maps ² 2-, 3-, and 4-variable maps ² 5- and 6-variable maps ± Primary implicants and function covers ± Consensus property ± Race conditions and hazards ² static-0 and static-1 glitches ² glitch-free design ± Iterated consensus ± Summary
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9/23/08 ESE218 Fall 2008 Lecture 7 2 AND-OR-invert (AOI) implementation • Note: Logic signals X,Y,W,Z propagate to output F through a single level of switches AND-NOR is a very fast implementation AOI (=AND-NOR) gate 0 0 R X Y W Z F • What switching function does it implement? • Consider the pull-down network presented with the pull-down networks of two NAND gates wired in parallel. Suppose they share the same pull-up network shown schematically with resistor R: the circuit on the left can be classified as an AOI (AND-OR-invert, AOI) gate. Analysis shows that it is F = (XY + WZ)’ After applying DeMorgan’s law: (X’+Y’)(W’+Z’) and distribution: X’W’ + Y’W’ + X’Z’ + Y’Z’ one can see that the circuit implements some SOP/POS
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9/23/08 ESE218 Fall 2008 Lecture 7 3 How to use the AOI gate? Suppose the function is specified in the SOP form: F(A,B,C) = A + B’C How to interconnect the AOI gate inputs with the function variables in order to implement the given switching function? 4 5 6 1 2 3 1 2 3 F AOI gate 0 0 R ? ? ? ? F Formally, one can consider it as the AND-OR implementation of some SOP form in front followed by inversion. A or A’? B or B’? C or C’?
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9/23/08 ESE218 Fall 2008 Lecture 7 4 AOI (AND-NOR) implementation It is beneficial to consider the complement to the function. It can be converted to the SOP form as follows: F’(A,B,C) = (A + B’C) = by DeMorgan’s = A’(B+C’) = by distribution = A’B + A’C’ A’ AND AND OR - NOT F B A’
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This note was uploaded on 03/21/2010 for the course ESE 218 taught by Professor Donetsky during the Fall '08 term at SUNY Stony Brook.

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218L7F08a - ESE218 Lecture 7. AOI and OAI implementations....

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