Binary to Decimal

Calculator

The following calculator will help you to convert a Binary number to a Decimal number.

Examples

In this example, we will convert a positive binary number (101) to a decimal number (5).

NumberCountCalculationSimplify
1 2 1 × 22 4
0 0 × 21 0
1 1 × 20 1
Total 5

101 (binary) = 5 (decimal)

Note: Count always starts from '0'.

Examples

In this example, we will convert a negative integer binary number (-1011) to a decimal number (-11).

NumberCountCalculationSimplify
1 3 1 × 23 8
0 0 × 22 0
1 1 × 21 2
1 1 × 20 1
Total 11

-1011 (binary) = -11 (decimal)

Note: Count always starts from '0'.

Explanation: For negative integer binary to decimal number, proceed the steps as same as positive integer binary to decimal number and finally multiply the output by '-1'.

Examples

In this example, we will convert a fractional binary number (10.1011) to a decimal number (2.6875).

Here, we have to split the fractional binary number into two parts.

  1. Integer part - 10
  2. Fraction part - 0.1011

Now, convert the Integer part of the given binary number (10) into a decimal number.

NumberCountCalculationSimplify
1 1 1 × 21 2
0 0 × 20 0
Total 2

10 (binary) = 2 (decimal)

Note: Count always starts from '0'.

Now, convert the Fraction part of the given decimal number (0.1011) into a binary number.

NumberCountCalculationSimplify
1 4 1 × 2-1 0.5
0 0 × 2-2 0
1 1 × 2-3 0.125
1 1 × 2-4 0.0625
Total 0.6875

0.1011 (binary) = 0.6875 (decimal)

Now, add both the results

10.1011 = 2 + 0.6875

10.1011 (binary) = 2.6875 (decimal)

Useful links

Share this Page

Meet the Author