Binary to Decimal Converter — How to Convert Binary to Decimal

Understanding positional notation.

The binary system is a base-2 number system representing values using only two digits: 0 and 1. The decimal system is a base-10 system using ten digits (0-9). If you want to perform the opposite calculation, you can use our dedicated decimal to binary converter.

To convert from binary to decimal, we use the positional notation method. Each digit in a binary number represents a power of 2, starting with 2⁰ on the far right (least significant bit) and increasing by a power of one as you move left. For negative values, see how to convert signed binary to decimal, or learn how to group bits to convert binary to hexadecimal directly.

The conversion formula.

For any binary number with n digits, the conversion formula is:

Where d₀ is the rightmost digit, d₁ is the second digit from the right, and so on.

Step-by-step binary to decimal conversion examples.

Binary to decimal in code.

print(int("1011", 2))      # 11
print(int("11111111", 2))  # 255
print(int("10000000", 2))  # 128
print(int("10101", 2))     # 21

parseInt("1011", 2);      // 11
parseInt("11111111", 2);  // 255
parseInt("10000000", 2);  // 128
// Or using BigInt for large values:
Number(BigInt("0b" + "11111111")); // 255

#include <stdio.h>
#include <stdlib.h>
int main() {
    printf("%ld\n", strtol("1011", NULL, 2));      // 11
    printf("%ld\n", strtol("11111111", NULL, 2));  // 255
    return 0;
}

System.out.println(Integer.parseInt("1011", 2));      // 11
System.out.println(Integer.parseInt("11111111", 2));  // 255
System.out.println(Integer.parseInt("10000000", 2));  // 128