Discrete Mathematics CS 2610 February 19, 2009

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  

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

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

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

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

Circuit Design: XOR x y xy + xy 1 y x F Design a circuit that implements the XOR (the stairway lighting problem) xy + xy x y xy + xy

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

Circuit Design Design a circuit for xy + z