Convert Hexadecimal (hex) to Binary (binary) instantly. Hexadecimal to binary conversion.
| Unit | Name | Value |
|---|---|---|
| decimal | Decimal (Base 10) | — |
| binary | Binary (Base 2) | — |
| octal | Octal (Base 8) | — |
Example: FF (Hexadecimal) = 11111111 (Binary)
Method: Replace each hex digit with its 4-bit binary equivalent. E.g. A₁₆ = 1010₂, FF₁₆ = 11111111₂.
Hexadecimal is base-16; 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
| Hexadecimal (base 16) | 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 | |
| A | 1010 | Ten |
| B | 1011 | |
| C | 1100 | |
| D | 1101 | |
| E | 1110 | |
| F | 1111 | Max nibble (4-bit) |
| 10 | 10000 | One hex digit |
| 20 | 100000 | 2⁵ |
| 40 | 1000000 | 2⁶ |
| 80 | 10000000 | 2⁷ |
| FF | 11111111 | Max byte |
| 100 | 100000000 | 2⁸ |
| 200 | 1000000000 | 2⁹ |
| 400 | 10000000000 | 1 KiB |
| 800 | 100000000000 | 2 KiB |
| 1000 | 1000000000000 | 4 KiB |
| 8000 | 1000000000000000 | 32 KiB |
| FFFF | 1111111111111111 | Max 16-bit unsigned |
| 10000 | 10000000000000000 | 2¹⁶ |
| 100000 | 100000000000000000000 | 1 MiB (2²⁰) |
F→1111, E→1110, D→1101, C→1100, B→1011, A→1010, 9→1001...
F=1111, E=1110, A=1010 are the most common hex values.
No information is lost — hex and binary are perfectly interchangeable.
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 hexadecimal (base-16) system uses digits 0–9 and letters A–F (where A=10, B=11, C=12, D=13, E=14, F=15). Hexadecimal became the standard shorthand for binary in computing because exactly 4 bits = 1 hex digit, making byte values compact: 1 byte (8 bits) = 2 hex digits (00–FF).
Hex is ubiquitous in programming: memory addresses (0x7FFF0000), color codes (#FF5733), MAC addresses (AA:BB:CC:DD:EE:FF), IPv6 addresses, and error codes all use hex. The prefix '0x' in code signifies hexadecimal. Every programmer encounters hex daily.
Interesting fact: HTML/CSS color #FFFFFF (white) = RGB(255, 255, 255) = binary 11111111 11111111 11111111. The hex system makes this immediately readable — each pair of hex digits is one color channel. Web color #FF0000 is pure red: maximum red (FF=255), zero green (00), zero blue (00).
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.
Hexadecimal to binary is essential for reading memory addresses, color values, and binary file formats. Each hex digit expands to exactly 4 binary bits. FF₁₆ = 11111111₂. A₁₆ = 1010₂. Memorize 0–F in binary and you can convert any hex value instantly.
Use the converter above for any value. Results are exact — numeral base conversions involve no rounding or approximation.