Hexadecimal to Binary Converter
Free online tool to instantly convert hexadecimal (Base 16) to binary (Base 2). Includes quick conversion tables and step-by-step mathematical explanations.
How to convert Hexadecimal to Binary
Converting from Hexadecimal (Base 16) toBinary (Base 2) involves positional value evaluation.
Convert Hexadecimal to Decimal
Multiply each digit of the hexadecimal number by 16 raised to the power of its position index (starting from position 0 on the right). Sum all products together to obtain the decimal equivalent.
Convert Decimal to Binary
Divide the decimal value repeatedly by 2. Record the remainders after each division. The final binary representation is formed by reading the remainders in reverse order (bottom to top).
Hexadecimal to Binary Quick Conversion Table
Common values converted between Hexadecimal (Base 16) and Binary (Base 2):
| Decimal (10) | Hexadecimal (16) | Binary (2) |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 | 10 |
| 3 | 3 | 11 |
| 4 | 4 | 100 |
| 5 | 5 | 101 |
| 6 | 6 | 110 |
| 7 | 7 | 111 |
| 8 | 8 | 1000 |
| 9 | 9 | 1001 |
| 10 | A | 1010 |
| 11 | B | 1011 |
| 12 | C | 1100 |
| 13 | D | 1101 |
| 14 | E | 1110 |
| 15 | F | 1111 |
| 16 | 10 | 10000 |
| 32 | 20 | 100000 |
| 64 | 40 | 1000000 |
| 100 | 64 | 1100100 |
| 255 | FF | 11111111 |
Hexadecimal to Binary Frequently Asked Questions
Common questions and step-by-step mathematical answers about converting Hexadecimal (Base 16) to Binary (Base 2).
1How do you convert hexadecimal to binary?↓
Map each hex digit to 4 binary bits (e.g., A=1010, B=1011, ..., F=1111) and concatenate the nibbles.
2What is the method for hex to binary conversion?↓
Because 16 = 2⁴, every hex symbol translates directly into 4 binary bits without division or multiplication.
3How do you convert hexadecimal to binary manually?↓
Example with 5B₁₆: 5 = 0101, B = 1011 → 01011011₂ (or 1011011₂).
4What is A in binary?↓
A = 10₁₀ = 8 + 2 = 1010₂.
5What is F in binary?↓
F = 15₁₀ = 8 + 4 + 2 + 1 = 1111₂.
6What is FF in binary?↓
F = 1111 and F = 1111 → 11111111₂ (8 bits of 1s, decimal 255).
7Why does each hexadecimal digit represent four binary bits?↓
This exact power match makes hexadecimal the standard shorthand for binary nibbles.
8How do you convert hexadecimal fractions to binary?↓
Example: 0.A4₁₆ → A = 1010, 4 = 0100 → 0.10100100₂.
9What is the relationship between hexadecimal and binary?↓
Two hex characters represent exactly one 8-bit byte (0x00 to 0xFF).
10How do you convert large hexadecimal numbers to binary?↓
Example: 1A3F₁₆ → 0001 1010 0011 1111 → 1101000111111₂.