Logic Circuits

Boolean algebra is ideal for expressing the behavior of logic circuits.

A circuit can be expressed as a logic design and implemented as a collection of individual connected logic gates.

Fixed Logic Systems

A fixed logic system has two possible choices for representing true and false.

Positive Logic

In a positive logic system, a high voltage is used to represent logical true (1), and a low voltage for a logical false (0).

Negative Logic

In a negative logic system, a low voltage is used to represent logical true (1), and a high voltage for a logical false (0).

In positive logic circuits it is normal to use +5V for true and 0V for false.

Switching Circuits

The abstract logic described previously can be implemented as an actual circuit. Switches are left open for logic 0 and closed for logic 1.

Two variable AND circuit X.Y

Two variable OR circuit X + Y

Four variable circuit U.V.(X + Y)

Truth Table

A truth table is a means for describing how a logic circuit's output depends on the logic levels present at the circuit's inputs.

In the following twos-inputs logic circuit, the table lists all possible combinations of logic levels present at inputs X and Y along with the corresponding output level F.

 X Y F = X*Y 0 0 0 0 1 0 1 0 0 1 1 1

When either input X AND Y is 1, the output F is 1. Therefore the "?" in the box is an AND gate.