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__

__L__

__adder Diagram__

__Boolean Equation__

**A=B.C**

**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**

**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__

**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__

**XOR Gate**
If only one input is

**true**then the output will be**true**.__Logic Diagram__

__Truth Table__

__Ladder Diagram__

__Boolean Equation__

**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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