# Fundamental Digital Electronics/Digital Subtractor

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## Half Subtractor[edit]

The half-subtractor is a combinational circuit which is used to perform subtraction of two bits. It has two inputs, X (minuend) and Y (subtrahend) and two outputs D (difference) and B (borrow).

## Truth Table[edit]

The truth table for the half subtractor is given below. ^{[1]}

X | Y | D | B |
---|---|---|---|

0 | 0 | 0 | 0 |

0 | 1 | 1 | 1 |

1 | 0 | 1 | 0 |

1 | 1 | 0 | 0 |

From the above table one can draw the Karnaugh map for "difference" and "borrow".

## Full Subtractor[edit]

The Full_subtractor is a combinational circuit which is used to perform subtraction of three bits. It has two inputs, X (minuend) and Y (subtrahend and Z ([[subtrahend]) and two outputs D (difference) and B (borrow).

## Truth Table[edit]

The truth table for the full subtractor is given below. ^{[2]}

X | Y | Z | D | B |
---|---|---|---|---|

0 | 0 | 0 | 0 | 0 |

0 | 0 | 1 | 1 | 1 |

0 | 1 | 0 | 1 | 1 |

0 | 1 | 1 | 0 | 1 |

1 | 0 | 0 | 1 | 0 |

1 | 0 | 1 | 0 | 0 |

1 | 1 | 0 | 0 | 0 |

1 | 1 | 1 | 1 | 1 |

So, Logic equations are D = (X xor Y)xor Z, B = (Z and (not(X xor Y)))or ((not X)and Y)