Logic gates, Boolean equation and equivlent ladder diagram

Boolean algebra was developed in the 1800’s by James Bool, an Irish mathematician. It was found to be extremely useful for designing digital circuits, and it is still heavily used by electrical engineers and computer scientists. The techniques can model a logical system with a single equation. The equation can then be simplified and/or manipulated into new forms. The same techniques developed for circuit designers adapt very well to ladder logic programming.

AND Gate

The AND gate requires two inputs and has one output. If here 0 is called false and 1 is called true the gate acts in the same way as the logical and operator. The output is true when both inputs are true. Otherwise, the output is false.

Logic Diagram

Truth Table

Ladder Diagram

Boolean Equation

A=B.C

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OR Gate

The output will be true if any of the input is true.

Logic Diagram

Truth Table

 Ladder Diagram

Boolean Equation

C=A+B

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NOR Gate

NOR gates out put are invert of OR gate. If both inputs are false then output will be true.

Logic Diagram

Truth Table

Ladder Diagram

Boolean Equation

 

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NAND Gate

NAND gates output are invert of AND gate. If both inputs are true then output will be true.

Logic Diagram

Truth Table

 Ladder Diagram

Boolean Equation

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XOR Gate

If only one input is true then the output will be true.

Logic Diagram

Truth Table

Ladder Diagram

Boolean Equation

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NOT Gate

The input and output is total opposite. If input is true output will be false, if input false output will be true. 

 Logic Diagram

Truth Table

 Ladder Diagram

Boolean Equation

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