Binary to Decimal Converter

How to convert binary to decimal

1. Write down the binary number and number each digit's position from right to left, starting at 0.
2. Multiply each digit (0 or 1) by 2 raised to the power of its position.
3. Add all the results together — that's your decimal number.

Example: 1011₂ = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = 8 + 0 + 2 + 1 = 11.

Background reading: the binary number system and two’s complement on Wikipedia.

Quick reference table

Powers of 2

int("1010", 2)   # → 10

parseInt("1010", 2); // → 10

#include <stdio.h>

int main(void) {
    const char *s = "1010";
    int result = 0;
    for (int i = 0; s[i] != '\0'; i++)
        result = result * 2 + (s[i] - '0');
    printf("%d\n", result);  /* → 10 */
    return 0;
}

Real-world applications

• Reading feature flags and file permissions in programming, where each bit switches something on or off.
• Understanding IP addresses and subnet masks, which are four 8-bit binary numbers.
• Debugging microcontrollers and hardware registers, which are read as raw binary.
• Learning how computers store numbers — the first topic in most computer science courses.

Common mistakes

• Adding the position values left-to-right as if they were decimal — bit values double from right to left.
• Thinking leading zeros change the value — 00101 is still 5.
• Losing track of place in long strings — group bits in fours to stay accurate.

Frequently asked questions

Need the reverse? Try our decimal to binary converter.