# Binary Addition & Subtraction with Examples (Especially for GATE-Geospatial 2022)

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## Introduction

We know that with the help of four basic arithmetic operations, namely, addition, subtraction, multiplication, and division, any mathematical operation can be performed. We know that multiplication is nothing but repeated addition and division is repeated subtraction. Subtraction can be performed by complementary addition. Hence, addition is the basic arithmetic operation.

## Binary Addition

The binary addition follows the same principle as in decimal addition, in the sense that when the sum of augend bit and addend bit is equal to the binary base value, then a carry is generated and the sum is zero.

Simple, using a form of carrying:

The results of sum operation on two 1-bit numbers are shown in the following example.

### Example: Results of Addition of Two 1-Bit Numbers

Number-A | Number-B | Sum | Carry |

0 | 0 | 0 | 0 |

0 | 1 | 1 | 0 |

1 | 0 | 1 | 0 |

1 | 1 | 0 | 1 |

### Example: Results of Addition of Two Multiple-Bit Numbers at I-Bit Position

Sum | Carry | |||

0 | 0 | 0 | 0 | 0 |

0 | 0 | 1 | 1 | 0 |

0 | 1 | 0 | 1 | 0 |

0 | 1 | 1 | 0 | 1 |

1 | 0 | 0 | 1 | 0 |

1 | 0 | 1 | 0 | 1 |

1 | 1 | 0 | 0 | 1 |

1 | 1 | 1 | 1 | 1 |

## Binary Subtraction

In case of binary subtraction, if the effective subtrahend at any bit position is greater than minuend at that bit position and 1 is added with the subtrahend bit of the next higher bit position.

Subtraction works in much the same way:

### Example: Subtract 9 Decimal from 22 Decimal in Binary

In binary,