Construct the truth table for this combination of gates:

To which three-input gate is this equivalent?

Construct the truth table by considering all possible combinations of inputs, followed by determining the results of each dual-input gate.

D = | E = | F = | ||||
---|---|---|---|---|---|---|

A | B | C | B' | A+B' | B^{.}C |
(D^{.}E)' |

0 | 0 | 0 | 1 | 1 | 0 | 1 |

0 | 0 | 1 | 1 | 1 | 0 | 1 |

0 | 1 | 0 | 0 | 0 | 0 | 1 |

0 | 1 | 1 | 0 | 0 | 1 | 1 |

1 | 0 | 0 | 1 | 1 | 0 | 1 |

1 | 0 | 1 | 1 | 1 | 0 | 1 |

1 | 1 | 0 | 0 | 1 | 0 | 1 |

1 | 1 | 1 | 0 | 1 | 1 | 0 |

This is equivalent to a three-input NAND gate.

"http://www.physics.udel.edu/~watson/phys345/quiz/08soln.html"

Last updated November 4, 1999.

Copyright George Watson, Univ. of Delaware, 1999.