Hex to Binary Converter
Convert any hexadecimal value to binary instantly — hex to binary is the one base conversion that's a direct digit lookup, no arithmetic required.
How to Convert Hex to Binary
Hex to binary is the simplest base conversion there is, because it's a direct lookup rather than arithmetic: each hex digit maps to exactly 4 binary bits (a "nibble"), so you convert one digit at a time and concatenate the results.
No addition, multiplication, carrying, or borrowing is involved — unlike converting hex to or from decimal, which does require real arithmetic at every step.
Hex to Binary Example, Step by Step
A3 = 10100011
A3 (hex) = 10100011 (binary)
A -> 1010 3 -> 0011 Concatenate: 1010 0011
| Step | Description | Result |
|---|---|---|
| Convert A | A is the 4-bit nibble for decimal 10 | 1010 |
| Convert 3 | 3 is the 4-bit nibble for decimal 3 | 0011 |
| Concatenate | join the nibbles in order | 10100011 |
Both nibbles here use all 4 bits, so nothing gets dropped. That won't always happen — see the FAQ on leading zeros for what changes when the first digit is small.
Hex Digit to Binary Nibble Reference
The full lookup table — memorize this once and hex-to-binary conversion becomes instant.
| Hex | Binary | Hex | Binary |
|---|---|---|---|
| 0 | 0000 | 8 | 1000 |
| 1 | 0001 | 9 | 1001 |
| 2 | 0010 | A | 1010 |
| 3 | 0011 | B | 1011 |
| 4 | 0100 | C | 1100 |
| 5 | 0101 | D | 1101 |
| 6 | 0110 | E | 1110 |
| 7 | 0111 | F | 1111 |
Where Hex to Binary Actually Comes Up
Expanding a Register's Flag Bits
Hardware status and control registers pack multiple on/off flags into one hex value — expanding it to binary lets you read each flag's state directly against the datasheet's bit layout.
0x85 -> 10000101
Cross-Referencing a Datasheet's Bit Diagram
Many chip datasheets document opcodes and configuration values as binary bit diagrams — converting the hex value from your code to binary lets you line it up against that diagram directly.
0x1A -> 00011010
Verifying a Bitmask by Eye
Confirming a hex bitmask covers exactly the bits you intend is far easier visually in binary than by mentally converting each hex digit — this makes the mask's shape immediately obvious.
0xF0 -> 11110000
Common Mistakes When Converting Hex to Binary
- Forgetting to pad each nibble to 4 bits when converting by hand — writing "1" instead of "0001" for the digit 1.
- Losing track of digit order when concatenating several nibbles together.
- Converting to decimal first as an unnecessary detour — hex to binary never needs to pass through decimal.
- Expecting the calculator's output to always be a multiple of 4 bits — the leading digit's unused leading zeros are dropped, same as any number.
Why Use This Calculator Instead of the Lookup Table Yourself
- Converts values of any length at once, not one nibble at a time
- Runs entirely in your browser — nothing you type gets sent anywhere
- Gives decimal and octal for the same value alongside the binary result
- Skips the error-prone step of manually concatenating nibbles in order
Frequently Asked Questions
How do you convert hex to binary manually?
Look up each hex digit's 4-bit binary equivalent (0-F maps to 0000-1111) and write them side by side in order — no addition, multiplication, or carrying involved, unlike converting to or from decimal.
Why does each hex digit become exactly 4 bits?
Because 16 (hex's base) is 2^4. Four binary digits can represent exactly 16 values (0000 through 1111), which lines up one-to-one with hex's 16 digits (0-F).
Does the calculator pad the result with leading zeros?
No — it shows the plain numeric value, so the very first digit's leading zeros are dropped, the same way decimal numbers don't display leading zeros. FF shows as 11111111, but a value like 0F shows as 1111, not 00001111.
Why is hex used as shorthand for binary in programming?
Because the digit-for-nibble mapping is exact and lossless, hex lets you write and read long binary values in a quarter of the characters without doing any real conversion math in your head.
Can I convert a hex color code to binary the same way?
Yes — a color like #2563EB converts digit by digit exactly like any other hex value; each pair of hex digits (one color channel) becomes 8 bits.
How many bits does a hex value with N digits have?
Up to 4 x N bits — a 2-digit hex value like FF is at most 8 bits, a 4-digit value like FFFF is at most 16 bits, and so on.
How do I expand a hex flags register into individual bit flags?
Convert the register value to binary here, then read each bit position left to right — each 1 marks a flag that's set, matching the bit layout most hardware datasheets document.
Is there a binary-to-hex table I can use in reverse for this?
Yes — the same nibble reference table below works in both directions, since hex-to-binary and binary-to-hex are exact inverses of the same lookup.