Agenda Lecture Content Combinatorial Circuits Boolean Algebras Exercise

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 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 = (x 1 x 2) x 3 is a Boolean expression

Combinatorial Circuits and Boolean Expression § Find the combinatorial circuits for the following boolean expressions: y = (x 1 (x 2 x 3 )) x 2

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