Decimal to Binary Converter

How to convert decimal to binary

1. Divide the decimal number by 2 and write down the remainder (0 or 1).
2. Divide the quotient by 2 and write down the new remainder.
3. Repeat until the quotient is 0, then read the remainders from bottom to top.

Example: 13 → 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1 → 1101.

Background reading: the binary number system on Wikipedia.

Quick reference table

Powers of 2

bin(10)[2:]      # → '1010'

(10).toString(2);  // → '1010'

#include <stdio.h>

int main(void) {
    int n = 10;
    char buf[33];
    int i = 0;
    if (n == 0) buf[i++] = '0';
    while (n > 0) { buf[i++] = '0' + (n % 2); n /= 2; }
    buf[i] = '\0';
    for (int j = i - 1; j >= 0; j--) putchar(buf[j]);  /* → 1010 */
    putchar('\n');
    return 0;
}

Real-world applications

• Setting Unix file permissions with chmod, where 7 = 111 grants read, write and execute.
• Building bitmasks and feature flags in code.
• Deriving subnet masks from CIDR notation in networking.
• Teaching place value and powers of two in computer science classes.

Common mistakes

• Reading the remainders top-to-bottom — they must be read bottom-to-top.
• Stopping the divisions too early — keep going until the quotient reaches 0.
• Dropping leading zeros when a fixed width like 8-bit is required — 5 is 101, but 8-bit is 00000101.

Frequently asked questions

Need the reverse? Try our binary to decimal converter.