What this conversion means in practice
You already have values in Hexadecimal (hex) and need Binary (binary) for the same material, drawing, or dataset. The factor below is the exact reciprocal of the forward direction; use it when sources quote the “other” unit first.
Each hex digit maps to exactly four bits, so hex is a compressed view of binary. Converting hex → binary expands each digit without cumulative rounding error.
Use this when a memory dump or packet shows hex but your bitwise testbench wants raw bits.
Uneven hex lengths still work: the leftmost digit maps to its binary group without requiring zero-padding assumptions beyond standard positional rules.
Mnemonic: F₁₆ = 1111₂; A5₁₆ = 10100101₂.
How to convert hexadecimal to binary
Treat your input strictly as a base-16 integer: only digits valid for that base are allowed. The tool converts to an exact integer, then prints it in base 2.
Live example: …16 → …2
Unlike unit conversions with a single scale factor, radix conversion rebuilds the digit sequence. The “expand to decimal, then divide out the target base” algorithm matches what you learn in CS, automated here for any size.
Hexadecimal
Definition: Base 16: digits 0–9 plus A–F for ten through fifteen. One hex digit represents exactly four bits.
History and origin: Adopted widely in computing to shorten binary strings while preserving bit alignment.
Current use: Memory addresses, RGB colors (#RRGGBB), UUIDs, hashes, and debug output.
Binary
Definition: Base 2: positional notation using only the digits 0 and 1. Each place is a power of 2.
History and origin: Used formally since Leibniz; became central with Boolean logic and electronic switching.
Current use: Machine code, buses, flags, and any representation of bits in computing.
Hexadecimal to Binary conversion table
| Hexadecimal (base 16) | Binary (base 2) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| A | 1010 |
| FF | 11111111 |
| 10 | 10000 |
| FACE | 1111101011001110 |
| 100 | 100000000 |
Hexadecimal to Binary FAQ
Quick answers for Hexadecimal-to-Binary rounding (reverse workflow), precision, and common mistakes.
Why might binary length not be a multiple of 8?
Because the integer value may not fill complete bytes; pad only when your protocol defines a width.
Can I round-trip with binary-to-hex?
Yes on the paired pages with the same integer value and no width truncation.
Do spaces or separators matter?
Enter contiguous hex digits only; remove spaces before converting.