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Fundamentals of Logic - Coggle Diagram
Fundamentals of Logic
The Binary Concept
Two-State Logic
Logic 1: ON / True / High / Closed
Logic 0: OFF / False / Low / Open
Logic Gates
Function: Circuits with multiple inputs and one output
Truth Tables: Tabular representation of all possible input/output states
Decision Examples
AND Decision: High beam circuit (Light Switch + High Beam Switch)
OR Decision: Dome light circuit (Passenger Door + Driver Door)
Logic Gate Functions
AND Gate
Rule: Output is 1 only if all inputs are 1
Hardware: Switches connected in series
OR Gate
Rule: Output is 1 if one or more inputs are 1
Hardware: Switches connected in parallel
NOT (Inverter)
Rule: Output is always the inverse of the input
Symbolism: Indicated by a bar over the letter or a small circle (state indicator)
Specialized Gates
NAND / NOR: Inverted versions of AND and OR
XOR (Exclusive-OR): Output is 1 only if inputs are different (comparison logic)
Boolean Algebra
Mathematical Operators
AND: Multiplication (AB)
OR: Addition (A+B)
NOT: Overbar (A)
Algebraic Laws
Commutative Law: A + B = B + A
Associative Law: (A + B) + C = A + (B + C)
Distributive Law: A(B + C) = AB + AC
Logic Design
Converting Expressions: Building gate circuits from Boolean equations
Deriving Equations: Writing Boolean statements from logic diagrams
Hardwired vs. Programmed Logic
Hardwired Logic
Implementation: Physical relays and electrical interconnections
Structure: Fixed relay ladder schematics (Rails and Rungs)
Programmed Logic (PLC)
Language: Ladder Logic (Software-based)
Flexibility: Logic changes via software without rewiring
Ladder Elements
Input Symbols: Normally Open (NO) and Normally Closed (NC) contacts
Output Symbols: Relay coil equivalents
Word-Level Logic Instructions
Bitwise Operations
Scope: Performs logic on entire 16-bit or 32-bit words (INT, DINT)
Instruction Set
AND / OR: Used to identify matching bit states across words
NOT: Inverts the entire bit pattern of a source word
XOR for Diagnostics
Function: Compares real-world inputs against desired states
Result: Mismatches energize corresponding bits in the destination word
Circuit Conversion
Logic to Boolean
Writing equations from gate diagrams
Boolean to Logic
Building gate circuits from equations