The **binary system** It is made up of two digits or elements 0 and 1. It is also known as **base system 2**, since they use powers of two to represent the numbers. Example:

1101 → 1 × 2^{3 }+ 1 × 2^{2 }+ 0 × 2^{1 }+ 1 × 2^{0}

In decimal form it would be expressed:

8 + 4 + 1 = 13 = 1101

In the binary system 1101 represents 13 in the decimal system.

**Sum of binary numbers**

We must follow the following rules:

**0 + 0 = 0**

**0 + 1 = 1**

**1 + 0 = 1**

**1 + 1 = 10**

**Example**:

- We start from right to left, add 1 + 1 = 10, put 0 and bring 1 (red).
- In the next column we add 1 (red) + 0 = 1 and 1 + 1 = 10, we put zero and we take 1 (red) ,.
- Third column 1 (red) + 1 = 10 and 10 + 0 = 10, we put the 0 and take 1 (red).
- Fourth column 1 (red) + 1 = 10 and 10 + 1 = 11, we put 1 and take 1 (red).
- Fifth column 1 (red) + 1 = 10 and 10 + 0 = 10, we put 0 and take 1 (red).
- Sixth column, 1 (red) + 0 = 1 and 1 + 1 = 10, we put 0 and take 1 (red).
- Seventh column, 1 (red) + 0 = 1 and 1 + 1 = 10, we finally put 10.

**Subtraction of binary numbers**

The subtraction has the following rules:

**0 - 0 = 0**

**1 - 0 = 1**

**1 - 1 = 0**

**0 - 1 = 1 takes 1**

**Example**:

- We start from right to left, we subtract 1 - 0 = 1 we put 1.
- Next column 1 - 1 = 0 we place 0.
- Third column 0 - 1 = 1 but let's take 1 (red) to the next column, we put 1.
- Fourth column 1 (red) - 0 = 1, but we take 1 (red) to the next column, 1 - 1 = 0 we put 0.
- Fifth column 1 (red) - 0 = 1 we take 1 (red) for the next column, 1 - 1 = 0 we put 0.
- Sixth column 1 (red) - 1 = 0 and 0 - 0 = 0, we put 0.
- Seventh column 1 - 0 = 1 we put 1.
- Eighth column 0 - 0 = 0 we put 0.
- Ninth column 0 - 0 = 0 we finally put 0.

**Multiplication of binary numbers**

Binary multiplication is obtained in the same way as decimal multiplication.

**Example**:

**Division of binary numbers**

The division of binary numbers has the same procedure of the decimal system that we know.

**Example**: