Math
Hex to Binary Converter
Enter a hex number and the converter replaces each digit with its 4-bit binary pattern, then joins the groups.
The nibble table shows every digit next to its bits so you can do the conversion by eye next time, and the decimal and octal values are included for checking.
Digits 0-9 and A-F (either case). A hex point is allowed (F.8). A 0x prefix is fine.
Try an example
Result
Converted value
—
- Decimal
- —
- Binary
- —
- Hexadecimal
- —
- Octal
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the hex to binary converter solves
Because 16 = 2^4, every hexadecimal digit is exactly four binary digits. That means hex to binary needs no arithmetic at all: look up each digit's 4-bit pattern and write the patterns side by side. This converter shows the nibble table for your input and drops the leading zeros of the first group.
Hex to binary table
| 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 |
How to use it
- Type the hex number; upper or lower case, with or without 0x.
- Add a hex point for fractions (A.8 = 1010.1).
- Read the nibble table: each row is one hex digit, its decimal value, and its four bits.
- The binary answer drops leading zeros; the grouped version keeps all four bits per digit.
How to read the answer
The binary result is the exact same value written with 0s and 1s. The grouped form (nibbles separated by spaces) matches the hex digits one to one, which is the form you want for bit masks and register diagrams. The decimal value confirms both readings agree.
Common mistakes and edge cases
- Dropping leading zeros inside a nibble. 2 is 0010, not 10, when it sits before other digits.
- Converting through decimal by mistake. Going digit by digit is faster and cannot overflow.
- Letters beyond F are not hex digits; the converter names any invalid character.
- Fractional hex converts digit by digit as well: .8 = .1000, .4 = .0100.
Worked examples
Two-digit hex
2D
Converted value
101101
All ones
FF
Converted value
11111111
Fractional hex
A.8
Converted value
1010.1
Negative
−1F
Converted value
-11111
Zero
0
Converted value
0
Long address
DEADBEEF
Converted value
11011110101011011011111011101111
Invalid digit
1Z
Converted value
—
Frequently asked questions
How do you convert hex to binary?+
Replace each hex digit with its 4-bit binary pattern and write the groups in order. 2D → 0010 1101 → 101101. No multiplication is needed.
Why is one hex digit four bits?+
Sixteen values need four bits (2^4 = 16). That exact fit is why hex is the standard shorthand for binary.
What is FF in binary?+
FF = 1111 1111, eight ones, which equals 255 in decimal.
Should I keep the leading zeros?+
Keep them when the bit width matters (a byte 0A is 0000 1010). Drop them when you just want the numeric value (1010).
Can I convert a hex fraction?+
Yes. Digits after the point convert the same way: A.8 = 1010.1000 = 1010.1.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
Related calculators
Binary to Hex Converter
Convert binary to hex by grouping bits into nibbles from the right, padding the first group, and reading each group as one hex digit. Shows the grouping table plus decimal and octal.
Hex to Decimal Converter
Convert hexadecimal to decimal with the place-value table (digit × 16^n), the digit-to-value key for A-F, nibble grouping into binary, and signed two's complement reading.
Decimal to Binary Converter
Convert decimal to binary with the repeated-division steps, fractional parts by repeated multiplication (0.625 → 0.101), repeating-fraction detection, and negatives as a sign or two's complement.
Octal Converter
Convert octal to binary, decimal, or hex and back, with the 3-bit grouping table (one octal digit = three bits), repeated division by 8, and fractional octal support.
Bitwise Calculator
AND, OR, XOR, NOT, NAND, and NOR on binary, decimal, octal, or hex inputs at 4 to 64 bits, with an aligned bit grid, a bit-by-bit truth table, and the result in every base.
Decimal to Hex Converter
Convert decimal to hexadecimal with the repeated-division-by-16 steps, remainders mapped to A-F, fractional parts, nibble grouping, and negatives in two's complement.
Last updated: September 4, 2026