signed binary number can be represented in one of the three ways

- Signed magnitude representation
- 1’s complement representation
- 2’s complement representation

Signed magnitude representation :

- If the data has positive as well as negative numbers then the signed binary number should be used.
- the + or – signs are represented in the form of binary by using 0 or 1. So 0 is used to represent the ( + ) sign and 1 is used to represent the ( – ) sign.
- the MSB of a binary number is used to represent the sign and the remaining bits are used to represent the magnitude.

8-bit signed binary numbers are shown in fig

(a) Positive binary number

(b) Negative binary number

8-bit signed binary numbers

Advantage of sign magnitude numbers:

- the main advantage of sign magnitude number is their simplicity.
- we can easily find the magnitude by deleting the sign bit.

Disadvantage of sign magnitude numbers: sign magnitude numbers have a limited use because the require complected circuits. these numbers are often used in analog to digital converter.

Complements: Complements are used in the digital computer. it is used to simplify the subtraction operation and for the logical manipulations.

* Note:- we take 1’s and 2’s complement only -ve numbers not +ve numbers.

Decimal |
Signed 2’s complement |
Signed 1’s complement |
Signed magnitude |

+ 7 |
0111 |
0111 |
0111 |

+ 6 |
0110 |
0110 |
0110 |

+ 5 |
0101 |
0101 |
0101 |

+ 4 |
0100 |
0100 |
0100 |

+ 3 |
0011 |
0011 |
0011 |

+ 2 |
0010 |
0010 |
0010 |

+ 1 |
0001 |
0001 |
0001 |

+ 0 |
0000 |
0000 |
0000 |

– 0 |
— |
1111 |
1000 |

– 1 |
1111 |
1110 |
1001 |

– 2 |
1110 |
1101 |
1010 |

– 3 |
1101 |
1100 |
1011 |

– 4 |
1100 |
1011 |
1100 |

– 5 |
1011 |
1010 |
1101 |

– 6 |
1010 |
1001 |
1110 |

– 7 |
1001 |
1000 |
1111 |

– 8 |
1000 |
— |
— |

Signed Binary Number

Signed Binary Arithmetic:- Addition in 2’s complement method there are four cases

1. Both numbers are +ve

2. +ve number and smaller -ve number

3. +ve number and larger -ve number

4. both number are -ve.

Case 1: Addition of both positive number:

Case 2: +ve number and smaller -ve number:

- find the 2’s complement of the smaller -ve number
- Add the +ve number with 2’s complement of smaller -ve number.
- The above sum must produse a carry. this carry is always discarded and the remaining bits give the +ve sum.

Let A = + 22 and B = -17

Case 3:- +ve number adds with larger -ve number

- find the 2’s complement to the larger -ve number
- Add the +ve number with 2’s complement of larger -ve number
- the above addition does not produce any carry. the result is a -ve number in the form of 2’s complement representation.

Case 4:- Both number have -ve number:-

- Both -ve number are represented in 2’s complement
- their addition produces a carry that will be discarded
- the remaining bits are the result of above addition in the 2’s complement representation.

Example:- -9 and -4