Binary To Decimal Converter


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How to convert a binary number to a decimal number?


To convert a binary number to decimal, multiply each binary digit by the matching power of 2, then add the values together. In short: digit x 2position. The example below shows how the positions are counted:

Binary Number: 1 0 1 1 . 1 0
Position of Digit: 3 2 1 0 . -1 -2
Digit * power of 2: 1*23 0*22 1*21 1*20 . 1*2−1 0*2−2

Imagine a binary number written as: dn-1 .... d4 d3 d2 d1 d0

The decimal value is the sum of each binary digit multiplied by the correct power of 2:

decimal = dn-1 x 2n-1 + .... + d1 x 21 + d0 x 20 + d-1 x 2-1 + .... + d-n x 2-n

Binary to decimal conversion


An example of binary to decimal conversion.


Convert (1011.10)2 to decimal.

binary number: 1 0 1 1 . 1 0
power of 2: 23 22 21 20 . 2−1 2−2

=(1011.10)2

= 1 x 23 + 0 x 22 + 1 x 21 + 1 x 20 + 1 x 2-1 + 0 x 2-2

= 8 + 0 + 2 + 1 + .5 + 0

= (11.5)10

Binary to decimal conversion table

Binary Decimal
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

Binary to decimal guide

Binary numbers use only 0 and 1. To convert binary to decimal, each digit is multiplied by a power of 2 based on its position, then the values are added.

Best uses

  • Check programming, networking, electronics, or computer science examples.
  • Convert base-2 homework problems step by step.
  • Verify binary values before using them in code or documentation.

Quality checks

  • Read positions from right to left for whole numbers.
  • Use negative powers of 2 for digits after a decimal point.
  • Confirm the input contains only 0, 1, and at most one decimal point.

Common mistakes

  • Reading binary like an ordinary decimal number.
  • Starting the rightmost whole-number position at 1 instead of 0.
  • Forgetting fractional binary places after the point.

Quick answers

What does 1011 mean in decimal?

1011 in binary equals 11 in decimal because it is 8 + 0 + 2 + 1.

Can binary have decimals?

Yes. Digits after the binary point use powers such as 2^-1, 2^-2, and 2^-3.