9/15/09 - l6 other gate typescopyright 2009 - joanne degroat, ece, osu1 other gate types
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9/15/09 - L6 Other Gate types Copyright 2009 - Joanne DeGroat, ECE, OSU 1
Other gate types
9/15/09 - L6 Other Gate types
Copyright 2009 - Joanne DeGroat, ECE, OSU 2
Class 9 outline Other gate types The XOR High Impedance
Material from section 2-8 thru 2-11 of text
Other gate types So far have seen
AND OR NOT
There are some other basic gates besides these
9/15/09 - L6 Other Gate types
Copyright 2009 - Joanne DeGroat, ECE, OSU 3
Other basic gates The Buffer F=X
The buffer is used when the signal needs redriven The Tri-State Buffer or 3-State Buffer
Useful for busses where there are multiple drivers
9/15/09 - L6 Other Gate types
Copyright 2009 - Joanne DeGroat, ECE, OSU 4
More basic gates – Very popular NAND – Not AND
NOR – Not OR
9/15/09 - L6 Other Gate types
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Complex Logic Gates XOR – Exclusive OR
F = XY’ + X’Y = X Y
XNOR – Exclusive NOR F = XY + X’Y’ = X Y
9/15/09 - L6 Other Gate types
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More complex logic gates AND-OR-INVERT (AOI)
F=(WX+YZ)’
OR-AND-INVERT (OAI) F = ( (W+X)(Y+Z) )’
9/15/09 - L6 Other Gate types
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And some more complex gates AND-OR
F = WX + YZ
OR-AND F = (W+X)(Y+Z)
9/15/09 - L6 Other Gate types
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More complex gates 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 - L6 Other Gate types
Copyright 2009 - Joanne DeGroat, ECE, OSU 9
Identities of the XOR operation The following identities apply to the XOR
operation: X 0 = X X 1 = X’ X X = 0 X X’ = 1 X Y’ = (X Y)’ X’ Y = (X Y)’
Any or all of these can be proven by truth table or algebraic manipulation
9/15/09 - L6 Other Gate types
Copyright 2009 - Joanne DeGroat, ECE, OSU 10
Another XOR relationship Show XNOR is the compliment of XOR.
(X Y)’ = X Y (XY’ + X’Y)’ = XY + X’Y’ Use DeMorgans (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 XY + X’Y’
9/15/09 - L6 Other Gate types
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XOR K-maps 2-variable map
Z = XY’+Y’X Z = X Y
3-variable map Z=XYZ
9/15/09 - L6 Other Gate types
Copyright 2009 - Joanne DeGroat, ECE, OSU 12
XOR K-maps (continued) 4-variable map
Z=WXYZ
Note that function is a one for an odd number of 1’s on the inputs
9/15/09 - L6 Other Gate types
Copyright 2009 - Joanne DeGroat, ECE, OSU 13
High Impedance Outputs Consider the following circuit with tri-state
buffers
9/15/09 - L6 Other Gate types
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Class 9 assignment Covered sections 2-8 thru 2-10 Problems for hand in
none Problems for practice
2-34
Reading for next class: none – midterm section 3-1 and 3-2 after midterm.
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