A * logic gate* is a basic or fundamental building block of a digital

*. Generally we discuss*

**circuit****logic gates**having two inputs and one output. At any instant, every terminal has one of the two binary conditions low (0) or high (1), represents voltage levels.

In most logic gates, the low state is approximately zero volts (0 V), while the high state is approximately positive five volts (+5 V). In logic gates we get output in Boolean either **true (1)** or **false (0)**.

**There are two types of logic circuits one is combinational and other is sequential logic circuit**

In digital circuit theory, **sequential logic** is a type of **logic** circuit whose output depends not only on the present value of its input signals but on the sequence of past inputs. While, **combinational logic devices are** those whose output depends only on present input. So logic gates are **combinational logic devices.**

**THERE ARE 7 LOGIC GATES WRITTEN BELOW**

**AND gate****OR gate****NOT gate**

NAND & NOR are **Universal Logic gates **because any Boolean function (all logic gates) can be implement without need of other gate type.

**NAND gate****NOR gate**

Exclusive Logic gates

**X-OR gate****X-NOR gate**

## BASIC LOGIC GATES

**AND GATE**

The AND operation in Boolean algebra is similar to the **multiplication** in ordinary algebra. The output Y is **“True”** (1) (HIGH) when both the inputs (A & B) are **“True”** (1) (HIGH). Otherwise, the output is “False” (0) (LOW). To understand it more clear check the truth table for two input AND gate. Symbol of AND gate shown below –

**Symbol AND Gate**

**Truth Table for Two Input AND Gate**

INPUT | Output of AND Gate | |
---|---|---|

A | B | Y = A . B |

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

**FOR EXAMPLE**

**OR GATE**

The OR operation in Boolean algebra is similar to the **addition** in ordinary algebra. The output **Y** is **“True”** (1) (HIGH) when **either** of the inputs (A or B) **or both** the inputs are **“True”** (1) (HIGH). If both the input are “False” (0) (LOW), only then the **output Y** is **False** (0) (LOW). To understand it more clear check the truth table for two input OR gate. Symbol of OR gate shown below –

**Symbol OR Gate**

Truth Table for Two Input OR Gate

__Truth Table for Two Input OR Gate__

INPUT | Output of OR Gate | |
---|---|---|

A | B | Y = A + B |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

**FOR EXAMPLE**

**NOT GATE**

The NOT operation in Boolean algebra is nothing but complementation or inverse of logic. For logic 0 gives 1 and for 1 gives 0. This operation is indicated by a bar “–” over the input variable. Symbol of NOT gate shown below –

**Symbol NOT Gate**

**Truth Table NOT Gate**

INPUT | Output of NOT Gate |
---|---|

A | Y = Ā |

0 | 1 |

1 | 0 |

## UNIVERSAL LOGIC GATES

**NAND GATE**

**The NAND gate** – NOT gate in-front of AND gate operation makes NAND gate (N-AND). The output Y is **“False”** (0) (LOW) when both the inputs (A & B) are **“True”** (1) (HIGH). Otherwise, the output is **“True”** (1) (HIGH). To understand it more clear check the truth table for two input AND gate. Symbol of AND gate shown below –

**Symbol NAND Gate**

Truth Table for Two Input NAND Gate

__Truth Table for Two Input NAND Gate__

**Comparison of NAND v/s AND gate**

INPUT | Output of NAND Gate | Output of AND Gate | |
---|---|---|---|

A | B | Y = A . B | A . B |

0 | 0 | 1 | 0 |

0 | 1 | 1 | 0 |

1 | 0 | 1 | 0 |

1 | 1 | 0 | 1 |

**NOR GATE**

**The NOR gate** – NOT gate in-front of OR gate operation makes NOR gate (N-OR). The output Y is **“True”** (1) (HIGH) when both the inputs (A & B) are **“False”** (0) (LOW). Otherwise, the output is **“False”** (0) (LOW). To understand it more clear check the truth table for two input NOR gate. Symbol of NOR gate shown below –

**Symbol NOR Gate**

**Truth Table for Two Input NOR Gate**

**Comparison of NOR v/s OR gate**

**
**

INPUT | Output of NOR Gate | Output of OR Gate | |
---|---|---|---|

A | B | Y = A + B | A + B |

0 | 0 | 1 | 0 |

0 | 1 | 0 | 1 |

1 | 0 | 0 | 1 |

1 | 1 | 0 | 1 |

## EXCLUSIVE LOGIC GATES

**XOR GATE**

The *XOR* ( *exclusive-OR* ) *gate* acts in the same way as the logical “either/or.” *The output is *** “True”** (1) (HIGH)

*if either, but not both, of the inputs are*

**(1) (HIGH). The output is**

*“True”***“False”**(0) (LOW) if both inputs are

**“False”**(0) (LOW) or if both inputs are

**“True”**(1) (HIGH).

Another way: *output is 1 if the inputs are different*, but* 0 if the inputs are the same*.

**Symbol XOR Gate**

Truth Table for Two Input XOR Gate

__Truth Table for Two Input XOR Gate__

INPUT | Output of XOR Gate | |
---|---|---|

A | B | Y = A ⊕ B = A . B +A . B |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

**XNOR GATE**

The *XNOR (exclusive-NOR) gate* is just a XOR gate followed by an inverter (NOT gate). Its output is **“True”** (1) (HIGH) if the inputs are the same, and **“False”** (0) (LOW) if the inputs are different.

Another way: *output is 1 if the inputs are same*, but* 0 if the inputs are the different*.

**Symbol X-NOR Gate**

Truth Table for Two Input X-NOR Gate

__Truth Table for Two Input X-NOR Gate__

**Using De Morgans’s Law A XNOR B**

INPUT | Output of XNOR Gate | Output of XOR Gate | |
---|---|---|---|

A | B | Y = A ⊕ B = (A +B ) . (A + B) | Y = A ⊕ B = A . B +A . B |

0 | 0 | 1 | 0 |

0 | 1 | 0 | 1 |

1 | 0 | 0 | 1 |

1 | 1 | 1 | 0 |

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