This operation is similar to the basic arithmetic subtraction performed on decimal numbers in Maths. Hence, when we subtract 1 from 0, we need to borrow 1 from the next higher order digit, to reduce the digit by 1 and the remainder left here is also 1.

The subtraction of binary numbers is given by:

Binary Number | Subtraction Value |

0 â€“ 0 | 0 |

1 â€“ 0 | 1 |

0 â€“ 1 | 1 (Borrow 1 from next high order digit) |

1 â€“ 1 | 0 |

When you borrow a number during subtraction, it becomes the number of the base you are subtracting from.

For example, in Base 2 if you borrow a number the number you borrow becomes 2.

Subtract the following:

**i.** 1001_{two} from 11001_{two}

**Explanation**

**1st Column (from right to left)** = 1 – 1 = 0. Write 0.

**2nd Column** = 0 – 0 = 0. Write 0.

**3rd Column **= 0 – 0 = 0. Write 0.

**4th Column** = 1 – 1 = 0. Write 0.

**5th Column** = 1 – 0 = 1. Write 1.

**ii.** 11011_{two } from 111010_{two}

**1st Column (from right to left) **= 0 is smaller than 1 so we will have to borrow from the 2nd column. Since it is in base 2 any number borrowed is 2. So borrowing two from the second column will give (2 + 0) – 1 = 1

**2nd Column** = This reduces 1 to 0 in the second column. 0 is smaller than 1 so we have to borrow again from the third column. We now have 2 – 1 = 1

**3rd Column** = This reduces 0 to -1 in the third column. This too is smaller than 1 so have to borrow from the 4th column. = 2 – 1 – 0 = 1

**4th Column **= This reduces 1 to 0 in the fourth column. We have to borrow from the 5th column. Remember that since we are subtracting in base 2 the number we borrow is 2. so we have 2 + 0 – 1 = 1

**5th Column** = This reduces 1 to 0 in the fifth column. We have to borrow from the 5th column.

So we have 2 + 0 – 1 = 1

**6th Column **= 1 is reduced to 0. The number in the 6th column is 0 so we can ignore it.

**Answer** = 11111_{2}

**iii.** 1101 -111

**1st Column (from right to left) ** = 1 – 1 = 0. Write 0.

**2nd Column** = 0 is smaller than 1 so we have to borrow from the third column. We are subtracting in base 2 so the number we borrow is 2. We therefore have 2 + 0 – 1 = 0

**3rd Column** = This reduces 1 to 0 in the third column. This too is smaller than 1 so have to borrow from the 4th column. We now have 2 + 0 – 1 = 1

**4th Column **= This reduces 1 to 0 in the fourth column. We don’t have to write anything down since what we have is 0.

**Answer** = 110_{2}

**iv. **1001_{two} – 1110_{two}

**v.** 1111_{two} – 101_{two}

A job well done. You are truly a blessing to the education sector.