For 2 logical inputs, there are 16 possible logic gates. Table 1 defines the 16 logic gates, shows logical symbol, behavior in symbolic logic, provides name, notes.

People are most familiar with the ones that are named: NAND, NOR, AND, OR, XOR. Table 1 includes these, as well as AND and OR gates with either input negated, logic 0 and logic 1(which aren't really logic gates), and some gates that aren't really binary.

Output when AB is | ||||||||

Gate # | 00 | 01 | 10 | 11 | Symbolic Logical Description | Symbol | Name/Description | Note |

0 | 0 | 0 | 0 | 0 | 0 | Always zero | Not really a gate | |

1 | 0 | 0 | 0 | 1 | A & B | AND | ||

2 | 0 | 0 | 1 | 0 | A & ~B | A and Not B | Universal | |

3 | 0 | 0 | 1 | 1 | A | A | Not BInary | |

4 | 0 | 1 | 0 | 0 | ~A & B | B and Not A | Universal | |

5 | 0 | 1 | 0 | 1 | B | B | Not Binary | |

6 | 0 | 1 | 1 | 0 | (A & ~B) | (~A & B) | XOR | Also Not Equals Function | |

7 | 0 | 1 | 1 | 1 | A | B | OR | ||

8 | 1 | 0 | 0 | 0 | ~(A | B) | NOR | Universal | |

9 | 1 | 0 | 0 | 1 | (A & B) | (~A & ~B) | XNOR | Also Equals Function | |

10 | 1 | 0 | 1 | 0 | ~B | Not B | Not Binary | |

11 | 1 | 0 | 1 | 1 | A | ~B | A or Not B | Universal | |

12 | 1 | 1 | 0 | 0 | ~A | Not A | Not Binary | |

13 | 1 | 1 | 0 | 1 | ~A | B | B or Not A | Unversal | |

14 | 1 | 1 | 1 | 0 | ~(A & B) | NAND | Universal | |

15 | 1 | 1 | 1 | 1 | 1 | Always 1 | Not really a gate |

Examples (a)-(g) below demonstrate how one can use a universal gate (here, the NAND gate) to construct several other gates: