Convert Decimal (decimal) to Binary (binary) instantly. Decimal to binary conversion.
| Unit | Name | Value |
|---|---|---|
| binary | Binary (Base 2) | — |
| hex | Hexadecimal (Base 16) | — |
| octal | Octal (Base 8) | — |
Example: 10 (Decimal) = 1010 (Binary)
Method: Repeatedly divide by 2 and record remainders. E.g. 10÷2=5r0, 5÷2=2r1, 2÷2=1r0, 1÷2=0r1 → read remainders upward: 1010₂.
Decimal is base-10; Binary is base-2. Use the converter above for any value instantly.
Common values from 0 to 1,048,576 — powers of 2 and standard computing values
| Decimal (base 10) | Binary (base 2) | Notes |
|---|---|---|
| 0 | 0 | Zero |
| 1 | 1 | One |
| 2 | 10 | Two |
| 3 | 11 | |
| 4 | 100 | Four |
| 5 | 101 | |
| 6 | 110 | |
| 7 | 111 | |
| 8 | 1000 | Eight |
| 9 | 1001 | |
| 10 | 1010 | Ten |
| 11 | 1011 | |
| 12 | 1100 | |
| 13 | 1101 | |
| 14 | 1110 | |
| 15 | 1111 | Max nibble (4-bit) |
| 16 | 10000 | One hex digit |
| 32 | 100000 | 2⁵ |
| 64 | 1000000 | 2⁶ |
| 128 | 10000000 | 2⁷ |
| 255 | 11111111 | Max byte |
| 256 | 100000000 | 2⁸ |
| 512 | 1000000000 | 2⁹ |
| 1024 | 10000000000 | 1 KiB |
| 2048 | 100000000000 | 2 KiB |
| 4096 | 1000000000000 | 4 KiB |
| 32768 | 1000000000000000 | 32 KiB |
| 65535 | 1111111111111111 | Max 16-bit unsigned |
| 65536 | 10000000000000000 | 2¹⁶ |
| 1048576 | 100000000000000000000 | 1 MiB (2²⁰) |
Divide by 2, note the remainder (0 or 1). Read remainders bottom-to-top for the binary result.
Find the largest power of 2 ≤ your number. Set that bit, subtract, repeat.
Even numbers end in 0, odd numbers end in 1 in binary.
Converts between binary, hex, and decimal daily for debugging, bitmasking, and memory address analysis.
Learns number base conversions as a fundamental concept in computer architecture and digital logic courses.
Works with IP addresses, subnet masks, and MAC addresses in binary, decimal, and hex representations.
Programs microcontrollers using binary bit patterns and hex register values for hardware configuration.
Designs logic circuits using binary truth tables and checks hex values on oscilloscopes and analyzers.
Reads hex dumps, analyzes binary data, and decodes encoded strings during reverse engineering and forensics.
The decimal (base-10) number system uses ten digits (0–9) and is the universal numeral system for human mathematics, commerce, and everyday life. It is almost certainly based on the ten fingers of the human hand — 'digit' comes from the Latin digitus meaning finger.
The decimal system with positional notation and zero was developed in India (5th–7th century CE) and transmitted to Europe via Arabic mathematicians — which is why it is also called the Hindu-Arabic numeral system. It replaced Roman numerals in European commerce by the 16th century.
Interesting fact: Not all cultures chose base-10. Babylonians used base-60 (preserved in our 60 seconds, 60 minutes, 360 degrees). The Mayans used base-20. The Yuki people of California used base-8, counting the spaces between fingers rather than the fingers themselves.
The binary (base-2) number system uses only two digits: 0 and 1. Every number is represented as a sum of powers of 2. It is the fundamental language of all digital computers, since electronic circuits naturally represent two states — on/off, high/low voltage, magnetized/demagnetized.
Binary was formalized by Gottfried Wilhelm Leibniz in 1703, inspired by the ancient Chinese I Ching hexagrams. The modern use of binary in computing traces to Claude Shannon's 1937 master's thesis, which showed that Boolean algebra could be implemented with electrical circuits — the foundation of all digital logic.
Interesting fact: A single binary digit is a 'bit'; 8 bits = 1 byte. A standard 64-bit computer processor works with numbers up to 2⁶⁴ − 1 ≈ 18.4 quintillion simultaneously. The DNA genetic code, though not binary, encodes information in base-4 (ACGT) — life's own digital system.
Decimal to binary conversion underpins all computer data encoding. Divide by 2 repeatedly — 10→1010₂, 255→11111111₂. Powers of 2 give round binary numbers: 64=1000000₂, 128=10000000₂, 256=100000000₂.
Use the converter above for any value. Results are exact — numeral base conversions involve no rounding or approximation.