Binary to Decimal Converter
Enter a binary number below to convert it to a decimal.
Decimal Number:
Steps to Convert to Decimal
 
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How to Convert Binary to Decimal
The binary number system is a base 2 number system since it only uses the digits 0 and 1. On the other hand, decimal is a base 10 number system since it uses ten digits, 0 to 9.
Often you’ll need to convert a binary number to its decimal value since most people use the decimal system. Binary numbers are often used in computing applications.
To convert a binary number to a decimal, you can use the positional notation method. To use this method, multiply each digit in the binary number from the rightmost number to the left by 2 to the power of n, where n is the distance from the right.
So, reading the binary number from right to left, the furthest digit to the right is equal to the digit times 20. The digit that is one position from the right is equal to the digit times 21.
Binary to Decimal Formula
Thus, the binary to decimal formula is:
decimal number10 = (d0 × 20) + (d1 × 21) + … + (dn – 1 × 2n – 1)
In this formula, d0 is the binary digit furthest to the right, d1 is the digit one position from the right, and dn – 1 is the digit furthest to the left.

You can also use a tool like our binary calculator to convert to decimal or hex.
For Example, let’s convert the binary number 10110 to decimal.
decimal number10 = (1 × 24) + (0 × 23) + (1 × 22) + (1 × 21) + (0 × 20)
decimal number10 = 22
Binary to Decimal Conversion Video Tutorial
How to Convert Fractional Binary Numbers to Decimal
For real numbers that contain fractional values, you can use the positional notation system to convert as well. Start by using the method above to convert the whole portion of the number from binary to decimal.
Then, for the remaining fractional value, multiply each number to the right of the decimal point by 2 to the power of -1 times the distance from the decimal point plus 1. Ok, that sounds complicated but it’s easier than it sounds, let’s demonstrate.
decimal number10 = (d-1 × 2-1) + (d-2 × 2-2) + … + (d-n × 2-n)
For Example, let’s convert the binary number 0.101 to decimal.
decimal number10 = (1 × 2-1) + (0 × 2-2) + (1 × 2-3)
decimal number10 = (1 ÷ 21) + (0 ÷ 22) + (1 ÷ 23)
decimal number10 = 0.5 + 0 + 0.125
decimal number10 = 0.625
The calculator above can convert binary numbers to decimal, including fractional numbers like this one, along with negative numbers.
Binary to Decimal Conversion Table
The table below shows binary numbers and the equivalent decimal number values.
Binary Number | Decimal Number |
---|---|
0 | 0 |
1 | 1 |
10 | 2 |
11 | 3 |
100 | 4 |
101 | 5 |
110 | 6 |
111 | 7 |
1000 | 8 |
1001 | 9 |
1010 | 10 |
1011 | 11 |
1100 | 12 |
1101 | 13 |
1110 | 14 |
1111 | 15 |
10000 | 16 |
10001 | 17 |
10010 | 18 |
10011 | 19 |
10100 | 20 |
10101 | 21 |
10110 | 22 |
10111 | 23 |
11000 | 24 |
11001 | 25 |
11010 | 26 |
11011 | 27 |
11100 | 28 |
11101 | 29 |
11110 | 30 |
11111 | 31 |
100000 | 32 |
1000000 | 64 |
10000000 | 128 |
100000000 | 256 |
1000000000 | 512 |
10000000000 | 1024 |
100000000000 | 2048 |