Other gate types 91509 L 6 Other Gate

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Other gate types 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne

Other gate types 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 1

Class 9 outline o Other gate types The XOR High Impedance o Material from

Class 9 outline o Other gate types The XOR High Impedance o Material from section 2 -8 thru 2 -11 of text o o 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 2

Other gate types o So far have seen n o AND OR NOT There

Other gate types o So far have seen n o AND OR NOT There are some other basic gates besides these 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 3

Other basic gates o The Buffer n o F=X The buffer is used when

Other basic gates o The Buffer n o F=X The buffer is used when the signal needs redriven The Tri-State Buffer or 3 -State Buffer n Useful for busses where there are multiple drivers 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 4

More basic gates – Very popular o NAND – Not AND o NOR –

More basic gates – Very popular o NAND – Not AND o NOR – Not OR 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 5

Complex Logic Gates o XOR – Exclusive OR n n o F = XY’

Complex Logic Gates o XOR – Exclusive OR n n o F = XY’ + X’Y =XÅY XNOR – Exclusive NOR n n F = XY + X’Y’ =XÄY 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 6

More complex logic gates o AND-OR-INVERT (AOI) n o F=(WX+YZ)’ OR-AND-INVERT (OAI) n F

More complex logic gates o AND-OR-INVERT (AOI) n o F=(WX+YZ)’ OR-AND-INVERT (OAI) n F = ( (W+X)(Y+Z) )’ 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 7

And some more complex gates o AND-OR n o F = WX + YZ

And some more complex gates o AND-OR n o F = WX + YZ OR-AND n F = (W+X)(Y+Z) 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 8

More complex gates o o In general, complex gates are used to reduce the

More complex gates o o In general, complex gates are used to reduce the circuit complexity needed to implement the Boolean function. In VLSI land AND-OR is implemented as NAND-NAND 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 9

Identities of the XOR operation o The following identities apply to the XOR operation:

Identities of the XOR operation o The following identities apply to the XOR operation: n n o XÅ0=X X Å 1 = X’ XÅX=0 X Å X’ = 1 X Å Y’ = (X Å Y)’ X’ Å Y = (X Å Y)’ Any or all of these can be proven by truth table or algebraic manipulation 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 10

Another XOR relationship o Show XNOR is the compliment of XOR. n n n

Another XOR relationship o Show XNOR is the compliment of XOR. n n n n (X Å Y)’ = X Ä Y (XY’ + X’Y)’ = XY + X’Y’ Use De. Morgans (XY’)’(X’Y)’ = XY + X’Y’ (X’+Y)(X+Y’) = XY + X’Y’ X’X + X’Y’ + XY + YY’ = XY + X’Y’ 0 + XY + X’Y’ + 0 º XY + X’Y’ 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 11

XOR K-maps o 2 -variable map n n o Z = XY’+Y’X Z=XÅY 3

XOR K-maps o 2 -variable map n n o Z = XY’+Y’X Z=XÅY 3 -variable map n Z=X Å Y Å Z 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 12

XOR K-maps (continued) o 4 -variable map n Z=W Å X Å Y Å

XOR K-maps (continued) o 4 -variable map n Z=W Å X Å Y Å Z n Note that function is a one for an odd number of 1’s on the inputs 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 13

High Impedance Outputs o Consider the following circuit with tri-state buffers 9/15/09 - L

High Impedance Outputs o Consider the following circuit with tri-state buffers 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 14

Class 9 assignment o o Covered sections 2 -8 thru 2 -10 Problems for

Class 9 assignment o o Covered sections 2 -8 thru 2 -10 Problems for hand in n o Problems for practice n o none 2 -34 Reading for next class: none – midterm section 3 -1 and 3 -2 after midterm. 9/15/09 - L 6 Other Gate types Copyright 2009 - Joanne De. Groat, ECE, OSU 15

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