Agenda Lecture Content: Combinatorial Circuits Boolean Algebras Exercise & Review

Combinatorial Circuits

Combinatorial Circuits Computers / Electronic devices circuits: Input: 0 or 1 Output: 0 or 1 Circuits can be constructed using any basic element that has two different states. Combinatorial circuits have no memory  previous inputs and the states of the system do not affect the output of a combinatorial circuit. Combinatorial circuits can be constructed using solid-state devices, called gates.

Gates Input and output of electronic devices: {0,1} Gates: the basic elements of a circuit Utilize gates to design circuits that perform a variety of task

Gates Inverter OR gate AND gate XOR gate NAND gate NOR gate Multiple input gate

Gates x  y x  y x  y  z  … x  y  z  …

Logic Table of Gates

Combinatorial Circuits

How to draw the inputs

Interconnecting Combinatorial Circuits

Combinatorial Circuits and Boolean Expression Combinatorial circuits can be represented by a Boolean expression. y = (x1  x2)  x3 is a Boolean expression expression

Combinatorial Circuits and Boolean Expression Find the combinatorial circuits for the following boolean expressions: y = (x1  (x2  x3 ))  x2

Combinatorial Circuits and Boolean Expression

Logic Table

Write the Boolean Expression

Equivalent Combinatorial Circuits Two combinatorial circuits are equivalent, if they have identical outputs for given identical inputs (they have identical logic tables).

Equivalent Combinatorial Circuits