How to Convert Binary to Decimal

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 (2ⁿ):

Decimal = d₀×2⁰ + d₁×2¹ + d₂×2² + …

Using Positional Notation

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

Example:

Find the decimal value of 111001₂:

Binary Number	1	0	0	1	1	1	0	1
Power of 2	27	26	25	24	23	22	21	20

10011101₂ = 1⋅2⁷+0⋅2⁶+0⋅2⁵+1⋅2⁴+1⋅2³+1⋅2²+0⋅2¹+1⋅2⁰
                       = 128+0+0+16+8+4+0+1
                       = 157₁₀

Using Doubling

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

1. Write down the binary number.
   
   
2. Starting from the left, double your previous total and add the current digit.
   
   
3. Double your current total and add the next leftmost digit.
   
   
4. 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 = 3
3 x 2 + 1 = 7
7 x 2 + 0 = 14
14 x 2 + 1 = 29
29 x 2 + 1 = 59
59 x 2 + 1 = 119
119 x 2 + 0 = 238