Binary to Decimal Calculator

About Binary to Decimal Calculator

Binary (base 2) uses only 0 and 1. Each position represents a power of 2, from right to left.

How to use this calculator

1. Enter the binary number, such as 101101.
2. Make sure each digit is only 0 or 1.
3. Check the result in decimal, which is the base 10 form.
4. Use the step-by-step breakdown to see how each bit contributes to the total.

The formula explained

A binary number \((b_n...b_1b_0)_2\) is converted by adding each bit times its power of 2, so the formula computes the decimal value of the binary string. The rightmost bit is multiplied by \(2^0\), the next by \(2^1\), and so on.

• \(b_i\) = the bit at position i, which is either 0 or 1
• i = the position index of the bit, starting at 0 on the right
• n = the highest bit position in the binary number

Step by step method

1. Write the binary number and label the positions from right to left starting at 0.
2. Multiply each bit by its power of 2.
3. Add the results together.
4. The sum is the decimal number.

Worked example

Problem. Convert the binary number 101101 to decimal.

1. Label the bits from right to left: 1, 0, 1, 1, 0, 1.
2. Compute each place value: 1×2^5 = 32, 0×2^4 = 0, 1×2^3 = 8, 1×2^2 = 4, 0×2^1 = 0, 1×2^0 = 1.
3. Add them: 32 + 0 + 8 + 4 + 0 + 1 = 45.

Tips and common mistakes

• Start counting powers of 2 from the rightmost digit, because that digit is always \(2^0\).
• If a binary digit is anything other than 0 or 1, the number is not valid binary.

Frequently asked questions