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Logic Gates and Boolean algebra

An electronic circuits which are designed to represent the logical expression are known as logic circuits or logic gates (OR-Gate, AND Gate, NOT Gate, NOR-Gate, NAND Gate, X-OR gate and X-NOR Gate). A Boolean algebra deals with the Boolean value that is either 1 or 0.

Logic Gates

OR- Gate
It is a logical gate that receives two or more input signals and generates the only one output signal. It produces output signal as true when any one of the input signal is true otherwise it produces output signal as false.
The OR-Gate logical expression for two inputs A and B is given below.
Q=A+B
The OR-Gate Symbol and Truth Table is shown in figure.

Symbol

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Truth Table

Input

Output

A

B

Q =A + B

0

0

0

0

1

1

1

0

1

1

1

1

AND- Gate
It is a logical gate that receives two or more input signals and generates the only one output signal. It produces output signal as true when all of the input signals are true otherwise it produces output signal as false.
The AND-Gate logical expression for two inputs A and B is given below.
Q=A . B
The AND-Gate Symbol and Truth Table is shown in figure.

Symbol

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Truth Table

Input

Output

A

B

Q =A . B

0

0

0

0

1

0

1

0

0

1

1

1

NOT- Gate
It is a logical gate that receives only one input signal and generates the inverted version of input signal. It is also known as Inverter Circuit Gate.
The NOT-Gate logical expression for two input A is given below.
Q= A’ (Complement of A)
The NOT-Gate Symbol and Truth Table is shown in figure.

Symbol

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Truth Table

Input

Output

A

Q =A’

0

1

1

0

NOR- Gate
It is a logical gate also known as NOT OR gate. It produces output as the complement of OR-Gate. The output of the NOR-Gate is false if any one of the input signal is true and output is true if all input signals are false.
The NOR-Gate logical expression for two inputs A and B is given below.
Q=(A+B)’
The NOR-Gate Symbol and Truth Table is shown in figure.

Symbol

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Truth Table

Input

Output

A

B

Q =(A + B)’

0

0

1

0

1

0

1

0

0

1

1

0

NAND- Gate
It is a logical gate also known as NOT AND gate. It produces output as the complement of AND-Gate. The output of the NAND-Gate are true if any one of the input signal is false and output is false if all input signals are true.
The NAND-Gate logical expression for two inputs A and B is given below.
Q=(A.B)’
The NAND-Gate Symbol and Truth Table is shown in figure.

Symbol

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Truth Table

Input

Output

A

B

Q =(A.B)’

0

0

1

0

1

1

1

0

1

1

1

0

XOR- Gate
It is a logical gate also known as Exclusive OR gate. It receives two or more inputs and produces output that performs exclusive disjunction. The output of the XOR-Gate is true only when exactly one of the input signal is true otherwise the output is false.
The XOR-Gate logical expression for two inputs A and B is given below.
Q=A’.B+A.B’
The XOR-Gate Symbol and Truth Table is shown in figure.

Symbol

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Truth Table

Input

Output

A

B

Q =A’.B +A.B’

0

0

0

0

1

1

1

0

1

1

1

0

X-NOR Gate
It is a logical gate also known as Exclusive NOR gate. It receives two or more inputs and produces output as the complement of XOR Gate. The output of the X-N-XOR-Gate is true only when all of the input signals are true or all of the input signals are false otherwise the output is false.
The X-NOR-Gate logical expression for two inputs A and B is given below.
Q=A.B + A’.B’
The X-NOR-Gate Symbol and Truth Table is shown in figure.

Symbol

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Truth Table

Input

Output

A

B

Q =A.B + A’.B’

0

0

1

0

1

0

1

0

0

1

1

1



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