9/15/09 - L6 Other Gate typesCopyright Joanne DeGroat, ECE, OSU1 Other gate types

9/15/09 - L6 Other Gate types Copyright Joanne DeGroat, ECE, OSU2 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 Joanne DeGroat, ECE, OSU3

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 Joanne DeGroat, ECE, OSU4

More basic gates – Very popular NAND – Not AND NOR – Not OR 9/15/09 - L6 Other Gate types Copyright Joanne DeGroat, ECE, OSU5

Complex Logic Gates XOR – Exclusive OR F = XY + XY = X Y XNOR – Exclusive NOR F = XY + XY = X Y 9/15/09 - L6 Other Gate types Copyright Joanne DeGroat, ECE, OSU6

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 Copyright Joanne DeGroat, ECE, OSU7

And some more complex gates AND-OR F = WX + YZ OR-AND F = (W+X)(Y+Z) 9/15/09 - L6 Other Gate types Copyright Joanne DeGroat, ECE, OSU8

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 Joanne DeGroat, ECE, OSU9

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) Any or all of these can be proven by truth table or algebraic manipulation 9/15/09 - L6 Other Gate types Copyright Joanne DeGroat, ECE, OSU10

Another XOR relationship Show XNOR is the compliment of XOR. (X Y) = X Y (XY + XY) = XY + XY Use DeMorgans (XY)(XY) = XY + XY (X+Y)(X+Y) = XY + XY XX + XY + XY + YY = XY + XY 0 + XY + XY + 0 XY + XY 9/15/09 - L6 Other Gate types Copyright Joanne DeGroat, ECE, OSU11

XOR K-maps 2-variable map Z = XY+YX Z = X Y 3-variable map Z=X Y Z 9/15/09 - L6 Other Gate types Copyright Joanne DeGroat, ECE, OSU12

XOR K-maps (continued) 4-variable map Z=W X Y Z Note that function is a one for an odd number of 1s on the inputs 9/15/09 - L6 Other Gate types Copyright Joanne DeGroat, ECE, OSU13

High Impedance Outputs Consider the following circuit with tri-state buffers 9/15/09 - L6 Other Gate types Copyright Joanne DeGroat, ECE, OSU14

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. 9/15/09 - L6 Other Gate types Copyright Joanne DeGroat, ECE, OSU15