Sign and modulus is a coding system which allows both posotive and negative numbers to be represented in binary. This works by using one of the bits in the code to define whether or noth the number represented by the following bits, is positive or negative.

With the use of three bits, 8 different combinations are possible. In the case of regular binary, the possible numbers that can be represented in three bits are; 0, 1, 2, 3, 4, 5, 6, 7. In sign and modulous however, the eight possible numbers that can be represented are -3, -2, -1, -0, 0, 1, 2, 3.

For example, the three bit combination '101' in regular binary represents the number '5' (4 + 0 + 1 = 5). However, in sign and modulus, this represents the number '-1'. This is because, the first bit in the combination is a '1', meaning the number will be a negative. The following two bits are worked out like regular binary, in this case "0 + 1 = 1".

So:

Sign and Modulus |
Decimal |

000 | 0 |

001 | 1 |

010 | 2 |

011 | 3 |

111 | -3 |

110 | -2 |

101 | -1 |

100 | -0 |