A binary number is most preferred in modern computer engineers, networking and communication specialists, and other professionals. There are two ways to convert a binary number into a decimal number. Here is how you can convert binary to decimal.

The decimal number is equal to the sum of binary digits (d_{n}) times their power of 2 (2^{n}):

**Decimal** = *d*_{0}×2^{0} + *d*_{1}×2^{1} + *d*_{2}×2^{2} + …

**Using Positional Notation**

- Write down the binary number and list the powers of 2 from right to left.
- Multiply the positional value of binary with their digit and get the sum of these steps.

#### Example:

Find the decimal value of **111001 _{2}**:

Binary Number | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 |
---|---|---|---|---|---|---|---|---|

Power of 2 | 2^{7} |
2^{6} |
2^{5} |
2^{4} |
2^{3} |
2^{2} |
2^{1} |
2^{0} |

**10011101 _{2}** = 1⋅2

^{7}+0⋅2

^{6}+0⋅2

^{5}+1⋅2

^{4}+1⋅2

^{3}+1⋅2

^{2}+0⋅2

^{1}+1⋅2

^{0}= 128+0+0+16+8+4+0+1

=

**157**

_{10}## Using Doubling

This is a simple method to convert a binary number into a decimal number.

- Write down the binary number.
- Starting from the left, double your previous total and add the current digit.
- Double your current total and add the next leftmost digit.
- Continue doubling your current total and adding the next digit until you’ve run out of digits.

**Example:**

**11101110 _{2} = (238)_{10}**

0 x 2 + 1 = **1****1** x 2 + 1 = **33 **x 2 + 1 =

**7**

**7**x 2 + 0 =

**14**

14x 2 + 1 =

14

**29**

29x 2 + 1 =

29

**59**

59x 2 + 1 =

59

**119**

119x 2 + 0 =

119

**238**