1. Discrete Mathematics CS 2610
February 19, 2009

2. Logic Gates: the basic elements of circuits
Electronic circuits consist of so-called gates connected by wires x x
Inverter (NOT gate) X Y
X+Y
OR gate x xy
AND gate y

3. Multiway Logical Gates
Multiple Input AND, OR Gates x1
x1+x2 +… + xn x2 xn x1
x1x2 …  xn x2 xn

4. Combinational Circuits
Combinational Circuits are circuits in which the logical gates’ outputs depend on their current inputs only
No loops
No memory capabilities
No current state worries

5. Circuit Design
Design a circuit for xy + xy x y
xy + xy

6. Circuit Design 1 y x F
Design a circuit for xy + xy x y
xy + xy

7. Circuit Design: XOR x y xy + xy1 y x F
Design a circuit that implements the XOR (the stairway lighting problem)
xy + xy x y
xy + xy

8. Circuit Design (aside)
The stairway light switches: up
down up
Switch 2
down up
Switch 1
down
+ -

9. Circuit Design
Design a circuit for xy + z