Binary to Decimal Converter

From

Enter binary number

₂

Decimal result

Decimal number

₁₀

Decimal from signed 2's complement

₁₀

Hex number

₁₀

Decimal calculation steps

How to convert Binary to Decimal?

To convert a binary number to decimal, you calculate the weighted sum of the digits. In binary (base 2), each position represents a power of $2$, starting from the rightmost digit ($2^0$).

The Positional Value Method

Start from the right: Assign each digit a power of $2$, starting with $2^0$ ($1$), then $2^1$ ($2$), $2^2$ ($4$), $2^3$ ($8$), and so on.
Multiply: Multiply each binary digit by its assigned power of $2$.
Sum: Add all the results together to get the final decimal value.

Example: Convert $1101_2$ to Decimal

Binary Digit	Position Value (2n)	Calculation	Result
$1$	$2^3 = 8$	$1 \times 8$	$8$
$1$	$2^2 = 4$	$1 \times 4$	$4$
$0$	$2^1 = 2$	$0 \times 2$	$0$
$1$	$2^0 = 1$	$1 \times 1$	$1$

Sum: $8 + 4 + 0 + 1 = \mathbf{13}$

Therefore, $1101_2 = 13_{10}$.