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In this tutorial, you will learn step by step method used for the conversion of binary to decimal.

Binary number has its base as **2**. That means it has total of 2 digits that are **0** and **1**. Whereas
decimal number has its base as **10**. That means it has total of 10 digits, that are **0, 1, 2, ..., 8, 9**.

To convert any binary number say **101110** to decimal number, then we have to follow the rules as shown in
the box given below:

2^{n}.........2^{5}2^{4}2^{3}2^{2}2^{1}2^{0}32 16 8 4 2 1 1 0 1 1 1 0 (binary number) 32 8 4 2 (write value below 1 only) =32+8+4+2 (sum up all the values) =46

Therefore **(101110) _{2} = (46)_{10}**

Here are the steps that are used to convert binary to decimal as shown in above box:

- In first line, write
**2**^{n}.........2^{5}2^{4}2^{3}2^{2}2^{1}2^{0} - In second line, write the values of
**.........2**that will be^{5}2^{4}2^{3}2^{2}2^{1}2^{0}**......... 32 16 8 4 2 1** - And in third line, write the given binary number from right side. That is the last digit
of binary number should be written below
**2**or^{0}**1** - Finally in fourth line, below each and every 1, write down the values of second step in corresponding columns of 1's
- Now sum up all the values of fourth step
- The summation will be the equivalent decimal value of given binary number

To convert any number given in binary form or binary number system into a decimal number system, then coefficient of binary number are multiplied by the power of 2. Letâ€™s take an example.

Convert (110110)_{2} in binary form.

(110110)_{2} = ( ? )_{10}

= 1*2^{5} + 1*2^{4} + 0*2^{3} + 1*2^{2} + 1*2^{1} + 0*2^{0}

= 32 + 16 + 0 + 4 + 2

= ( 54 )_{10}

= 1*2

= 32 + 16 + 0 + 4 + 2

= ( 54 )

Therefore, 110110 in binary will be equal to 54 in decimal.

- Binary to Decimal in C
- Binary to Decimal in Python
- Binary to Decimal in Java
- Binary to Decimal in C++

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