# Binary to Decimal Formula

**Binary to Decimal Formula:**

N is decimal equivalent,

b is the digit,

q is the base value that starts from most significant digit order q

^{n}to least significant order q

^{-1}, q

^{-2}, …..

To convert binary to decimal the following chart is used and binary is noted as per the given decimal number.

Binary |
0 | 1 | 10 | 11 | 100 | 101 | 110 | 111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |

Decimal |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |

So, for instance, if you use a binary number string it should add the subscript “2” to denote a base 2 number so the binary number would be written as $10_{2}$. Likewise if it was a standard decimal number it would add the subscript “10” to denote a base 10 and written as $10_{10}$.

Say we want to convert the 8 bit value 10011101 into a decimal value, we can use a formula table like that below:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 |

To convert, you simply take a value from the top row wherever there is a 1 below and then add the values together.

### Solved Examples

**Question 1:**Convert 0110101 to decimal

**Solution:**

Given Binary number is 0110101

**0110101**= (0 $\times$ $2^{6}$) + (1 $\times$ $2^{5}$) + (1 $\times$ $2^{4}$) + (0 $\times$ $2^{3}$) + (1 $\times$ $2^{2}$) + (0 $\times$ $2^{1}$) + (0 $\times$ $2^{0}$)

= 0 + 32 + 16 + 0 + 4 + 0 + 0

= 52

**Answer:**Binary Number 0110101 = 52 Decimal number