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Fundamentals of Logic - Coggle Diagram
Fundamentals of Logic
AND, OR, and NOT Functions
AND Function
Requires all inputs to be 1 for output to be 1
Truth Table Representation
Circuit Representation (Series Connection)
OR Function
Output is 1 if at least one input is 1
Circuit Representation (Parallel Connection)
Truth Table Representation
NOT Function
Inverts the input (1 becomes 0, 0 becomes 1)
Also known as an Inverter
Used with AND and OR gates
Exclusive-OR (XOR) Function
Output is 1 when inputs are different
Used for binary comparisons
Truth Table and Logic Diagram
Boolean Algebra
Definition and Importance
Mathematical representation of logic
Simplifies PLC programming
Boolean Operators
AND (• or multiplication)
OR (+ or addition)
NOT (overline or inversion)
Boolean Equations in PLC Design
Example: Y = AB + C
Logic Gate Implementation
Basic Laws of Boolean Algebra
Commutative Law
Associative Law
Distributive Law
The Binary Concept
Binary Principle
Two-state system (1 and 0)
Used in PLCs and digital systems
Logic Decision Making
Example: High beam lighting circuit (AND logic)
Example: Dome light circuit (OR logic)
Representation of Binary States
ON/OFF, True/False, Open/Closed
Hardwired Logic vs. Programmed Logic
Hardwired Logic
Uses physical electrical connections
Requires rewiring for changes
Programmed Logic
Implemented via software
Uses ladder logic in PLCs
Relay Ladder Schematics
Example: Motor start/stop circuit
Conversion to Ladder Logic
Programming Word Level Logic Instructions
Logic Instructions
AND: Identifies matching 1s
OR: Identifies any 1s
XOR: Identifies differences
NOT: Inverts bit states
Word-Level Logic Operations
AND, OR, XOR, and NOT with word-sized data
PLC implementation
Bitwise Operations in PLC
Error diagnostics using XOR
Comparing Input/Output bits
Developing Logic Gate Circuits from Boolean Expressions
Steps in Circuit Development
Identifying required gates
Constructing logic circuits
Implementing in hardware or software
Applications in PLC Programming
Relay-based circuit conversions
Ladder logic representation
Producing the Boolean Equation for a Given Logic Gate Circuit
Analyzing Gate Outputs
Finding expressions for AND, OR, NOT gates
Simplification Techniques
Karnaugh Maps
DeMorgan’s Theorems