Convert a decimal number to binary: method and table

Easily convert decimal numbers to binary using the successive division method, a complete table and practical examples.

Published on January 22, 2026

Converting a decimal number to binary is a basic skill in computing and digital electronics. It is necessary to understand Unix permissions (chmod 755 = 111 101 101), network addresses, bitwise operations and the internal representation of data.

Understanding the conversion

The successive division by 2 method is the simplest for converting decimal to binary. Divide the number by 2 repeatedly, note the remainders (0 or 1) at each step, and read the remainders from bottom to top to get the binary representation. Alternatively, you can subtract successive powers of 2.

📐 Formula

Method: divide by 2 repeatedly → read remainders from bottom to top

📊 Conversion table

Decimal	Binary	Verification
0	0	—
1	1	1
5	101	4+1
10	1010	8+2
15	1111	8+4+2+1
16	10000	16
42	101010	32+8+2
100	1100100	64+32+4
255	11111111	128+64+32+16+8+4+2+1

💡 Practical examples

Example 1: convert 13 to binary

13 ÷ 2 = 6 remainder 1 → 6 ÷ 2 = 3 remainder 0 → 3 ÷ 2 = 1 remainder 1 → 1 ÷ 2 = 0 remainder 1. Read remainders bottom to top: 1101. Check: 8+4+1 = 13 ✓

Example 2: Unix chmod 755 permissions

7 → 111 (rwx), 5 → 101 (r-x), 5 → 101 (r-x). chmod 755 in binary = 111 101 101: read-write-execute for owner, read-execute for others.

Example 3: represent an IP byte

An IP address byte like 192: 192 = 128+64 = 11000000 in binary. Subnets and CIDR masks rely on this representation.