Decimal to Binary Converter

Decimal to Binary Converter — Free decimal to binary converter. Type any number in decimal, binary, octal, or hex and all four update instantly. Supports numbers up to 64-bit (18,446,744,073,709,551,615). No signup required.

Type in any field — all bases update instantly

—Decimal

—Bits

—Valid

Decimal

Binary

Octal

Hexadecimal

Try an example

Number bases explained

Computers store everything as binary — sequences of 0s and 1s. But working with long binary strings is tedious, so programmers also use octal (base-8) and hexadecimal (base-16) as more compact representations of the same values. This tool lets you convert between all four bases instantly.

Base	Digits used	Common use
Decimal (10)	0–9	Everyday numbers
Binary (2)	0, 1	CPU / memory / logic
Octal (8)	0–7	Unix file permissions
Hexadecimal (16)	0–9, A–F	Colors, memory addresses, byte values

Common values across bases

Decimal	Binary	Octal	Hex
0	0	0	0
1	1	1	1
8	1000	10	8
10	1010	12	A
15	1111	17	F
16	10000	20	10
42	101010	52	2A
255	11111111	377	FF
256	100000000	400	100
1024	10000000000	2000	400
65535	1111111111111111	177777	FFFF

How to convert decimal to binary manually

Divide the number by 2 repeatedly and record the remainders. Read the remainders bottom to top for the binary result.

Convert 42 to binary:

42 ÷ 2 = 21 remainder 0

21 ÷ 2 = 10 remainder 1

10 ÷ 2 = 5 remainder 0

5 ÷ 2 = 2 remainder 1

2 ÷ 2 = 1 remainder 0

1 ÷ 2 = 0 remainder 1

Read bottom to top: 101010

Why hex and octal group neatly with binary

One hex digit maps exactly to 4 binary bits. One octal digit maps exactly to 3 binary bits. This makes conversion between these bases trivial — no math required, just group the bits.

Binary: 1010 1111

Hex: A F → AF

Binary: 001 010 111

Octal: 1 2 7 → 127

Frequently Asked Questions

How do I convert decimal to binary?

Type your decimal number in the Decimal field — the binary equivalent appears instantly. For example: 10 → 1010, 255 → 11111111, 42 → 101010. You can also type in the Binary field to convert back to decimal.

What is binary?

Binary is base-2 — it uses only two digits: 0 and 1. Every number that computers process internally is ultimately stored as binary. Each digit is called a bit; 8 bits make a byte.

What is hexadecimal?

Hexadecimal (hex) is base-16. It uses digits 0–9 and letters A–F. Hex is compact — one hex digit represents exactly 4 binary bits. It's widely used in programming, color codes (#FF5733), and memory addresses.

What is octal?

Octal is base-8, using digits 0–7. Each octal digit represents exactly 3 binary bits. Octal was common in early computing and is still used in Unix file permissions (e.g. chmod 755).

What is the largest number this tool converts?

This tool supports numbers up to 64-bit unsigned integers — 18,446,744,073,709,551,615 in decimal, or FFFFFFFFFFFFFFFF in hex. That covers virtually all practical computing use cases.