**Category : **JEE Main & Advanced

(1) **The 'NAND' gate :** From 'AND' and 'NOT' gate

Boolean expression and truth table : \[Y=\overline{A\cdot B}\]

A | B | \[Y'=A\cdot B\] | Y |

0 | 0 | 0 | 1 |

0 | 1 | 0 | 1 |

1 | 0 | 0 | 1 |

1 | 1 | 1 | 0 |

(2) **The 'NOR' gate :** From 'OR' and 'NOT' gate

Boolean expression and truth table : \[Y=\overline{A+B}\]

A | B | \[Y'=A+B\] | Y |

0 | 0 | 0 | 1 |

0 | 1 | 1 | 0 |

1 | 0 | 1 | 0 |

1 | 1 | 1 | 0 |

(3) **The 'XOR' gate :** From 'NOT', 'AND' and 'OR' gate. Known as exclusive OR gate. or The logic gate which gives high output (i.e., 1) if either input A or input B but not both are high (i.e. 1) is called exclusive OR gate or the XOR gate. It may be noted that if both the inputs of the XOR gate are high, then the output is low (i.e., 0).

Boolean expression and truth table : \[Y=A\oplus B=\bar{A}B+A\overline{B}\]

A | B | Y |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

(4) The exclusive nor (XNOR) gate XOR + NOT \[\xrightarrow{\,\,\,\,\,\,\,\,\,\,}\] XNOR

Boolean expression : \[Y=A\odot =\bar{A}\,\bar{B}+AB\]

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