1. 9/15/09 - L6 Other Gate typesCopyright 2009 - Joanne DeGroat, ECE, OSU1 Other gate types

2. 9/15/09 - L6 Other Gate types Copyright 2009 - Joanne DeGroat, ECE, OSU2 Class 9 outline Other gate types The XOR High Impedance Material from section 2-8 thru 2-11 of text

3. 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, OSU3

4. 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, OSU4

5. More basic gates – Very popular NAND – Not AND NOR – Not OR 9/15/09 - L6 Other Gate types Copyright 2009 - Joanne DeGroat, ECE, OSU5

6. 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 2009 - Joanne DeGroat, ECE, OSU6

7. 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 2009 - Joanne DeGroat, ECE, OSU7

8. 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 2009 - Joanne DeGroat, ECE, OSU8

9. 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, OSU9

10. 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 2009 - Joanne DeGroat, ECE, OSU10

11. 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 2009 - Joanne DeGroat, ECE, OSU11

12. 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 2009 - Joanne DeGroat, ECE, OSU12

13. 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 2009 - Joanne DeGroat, ECE, OSU13

14. High Impedance Outputs Consider the following circuit with tri-state buffers 9/15/09 - L6 Other Gate types Copyright 2009 - Joanne DeGroat, ECE, OSU14

15. 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 2009 - Joanne DeGroat, ECE, OSU15