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**Logic gates:**

“Logic gates are digital circuits or electronic circuits that manipulate voltages, so, in effect, they manipulate the binary ones and zeros which are moving around inside your computer.”

Logic gates,
and the innovative ways in which they may be combined, are thus necessary for
the proper functioning of a digital computer.

**Boolean expression:**

“The relationship between input and
output is called boolean expression and is

represented in binary numbers.”

Binary numbers have only two possibilities. Zero and one. When dealing
with the circuits, zero corresponds with the circuit in off state and one corresponds
with the circuit in on state. So if we are dealing with true or false
statements zero is considered as false and one is considered true. If you
are dealing with voltage an off state would have zero volts and an on-stage
will have voltage more than zero.

**Types of logic gates:**

There
are basically seven types of logic gates which are further classified into
three groups:

●
Basic gates

●
Logic gates

●
Arithmetic gates

**Basic Gates:**

Basic gates are the type of gates that can not do anything individually. They have to combine with other gates to design a circuit. that is why they are called basic gates because they can not pass the voltage alone they have to combine with other gates to complete the circuit. Types of basic gates are

➢ OR

➢ AND

➢ NOT

**OR Gate:**

●
Or gate requires two inputs( A, B)and gives one output (Y).

●
The basic logic of this gate is that if at least one input is 1,
the output will be 1.

●
The mathematical equation of this gate is :

Y=A+B

**Symbol:**

**Truth table:**

A |
B |
Y |

0 |
0 |
0 |

0 |
1 |
1 |

1 |
0 |
1 |

1 |
1 |
1 |

**AND Gate:**

●
Just like or gate and gate requires single output and two
inputs.

●
The output of the and gate will be one only when all inputs
will be one

●
The mathematical equation of this gate is:

Y=A-B

**Symbol:**

**Truth table:**

A |
B |
Y |

0 |
0 |
0 |

0 |
1 |
0 |

1 |
0 |
0 |

1 |
1 |
1 |

**NOT Gate:**

●
NOT gate consists of one input and one output.

●
The output and input of this gate will be reversed from each
other. That is why it is also called the inverter.

●
The mathematical equation of this gate is

Y=A’

**Symbol:**

**Truth table:**

A |
Y |

0 |
1 |

1 |
0 |

** Universal Gates:**

Universal gates are formed by the
combination of two basic gates. Types of universal gates are

➢ NAND gate

➢ NOR gate

**NAND gate:**

●
A NAND gate essentially operates as an and gate followed by a
not gate. that is why it is also sometimes called the ‘NOT-AND’ gate

●
The output of this gate will be zero only if both of the
inputs will be one.

●
The mathematical equation of this gate is

Y=(A.B)’

**Symbol:**

**Truth table:**

A |
B |
Y |

0 |
0 |
1 |

0 |
1 |
1 |

1 |
0 |
1 |

1 |
1 |
0 |

**NOR gate:**

●
A nor gate is also sometimes called a ‘NOT-OR’ gate, which
is essentially or gate filled by not gate.

●
The output of this gate will be one only if both of the
inputs will be zero otherwise the output will be false.

●
The mathematical equation of this gate is

Y=(A+B)’** **

**Symbol:**

**Truth table:**

A |
B |
Y |

0 |
0 |
1 |

0 |
1 |
0 |

1 |
0 |
0 |

1 |
1 |
0 |

**Arithmetic Gates:**

Arithmetic
gates are the special type of gates that can be used in the half adder, full
adder, and subtractor. Types of these gates are

➢ XOR gate

➢ XNOR gate

**XOR Gate:**

●
The XOR gate or ‘Ex-OR’ basically consists of two inputs and
one output.

●
The output of this gate will be false if both of the inputs
are true.

●
The mathematical equation of this gate is

Y=A’.B+A.B’

**Symbol:**

**Truth
table:**

A |
B |
Y |

0 |
0 |
0 |

0 |
1 |
1 |

1 |
0 |
1 |

1 |
1 |
0 |

**XNOR Gate:**

●
The XNOR gate or ‘Ex-NOR’ accepts only one output but
more than one input.

●
The output of this gate will be one if both of the inputs are
the same and it will be zero if both inputs are different.

●
The mathematical equation f this gate is

Y=A.B+A’B’.

**Symbol:**

**Truth table:**

A |
B |
Y |

0 |
0 |
1 |

0 |
1 |
0 |

1 |
0 |
0 |

1 |
1 |
1 |

**Uses:**

● Nearly every digital device we use on a regular basis contains logic gates. Such as laptops, smartphones, tablets, memory devices, etc.

●
Logic gates can be combined in a million different
combinations and these number of combinations can be used to make different
technologies like robots etc.

●
Logic gates are basically the main component of a chip that
is used in different electronic devices.

● Commonly used logic gates are TTL, or Transistor-Transistor Logic, CMOS, or Complementary Metal-Oxide-Silicon and chips (ICs)

**De-Morgans
Theorem:**

**First Theorem:**

**Second Theorem:**

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