7.9 Converting Truth Tables into Boolean Expressions
In designing digital circuits, the designer often begins with a truth table describing what the circuit should do. The...
Tag: Free Book on Digital
7.8 DeMorgan’s Theorems
A mathematician named DeMorgan developed a pair of important rules regarding group complementation in Boolean algebra....
7.7 The Exclusive-OR Function: The XOR Gate
What Is a XOR Gate? One element conspicuously missing from the set of Boolean operations is that of Exclusive-OR, often...
7.6 Circuit Simplification Examples
Let’s begin with a semiconductor gate circuit in need of simplification. The “A,” “B,” and “C” input...
7.5 Boolean Rules for Simplification
Boolean algebra finds its most practical use in the simplification of logic circuits. If we translate a logic...
7.4 Boolean Algebraic Properties
The Commutative Property Another type of mathematical identity, called a “property” or a “law,” describes how...
7.3 Boolean Algebraic Identities
In mathematics, an identity is a statement true for all possible values of its variable or variables. The algebraic...
7.2 Boolean Arithmetic
Let us begin our exploration of Boolean algebra by adding numbers together: The first three sums make perfect sense to...
7.1 Introduction to Boolean Algebra
Mathematical rules are based on the defining limits we place on the particular numerical quantities dealt with. When we...
6.6 Programmable Logic Controllers (PLC)
Before the advent of solid-state logic circuits, logical control systems were designed and built exclusively around...
6.5 Fail-safe Design
Logic circuits, whether comprised of electromechanical relays or solid-state gates, can be built in many different ways...
6.4 Motor Control Circuits
The interlock contacts installed in the previous section’s motor control circuit work fine, but the motor will run...
6.3 Permissive and Interlock Circuits
A practical application of switch and relay logic is in control systems where several process conditions have to be met...
6.2 Digital Logic Functions
We can construct simple logic functions for our hypothetical lamp circuit, using multiple contacts, and document these...
6.1 Ladder Diagrams
Ladder diagrams are specialized schematics commonly used to document industrial control logic systems. They are called...
