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 DiagramBoolean Equation
A=B.C
OR Gate
The output will be true if any of the input is true.
Logic Diagram
Truth Table
Ladder DiagramBoolean 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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