Hex to Binary Converter
Convert hexadecimal to binary instantly with exact 4-bit digit mapping. Enter any valid hex integer to get its binary representation, grouped nibble breakdown, bit count, verified examples, and reference tables.
What Is a Hex to Binary Converter?
A hex to binary converter changes an integer from the hexadecimal number system (base 16) into the equivalent binary number system (base 2).
Hexadecimal uses sixteen digit values: 0 through 9 and A through F. Binary uses only 0 and 1. The two systems are strongly related because 16 = 2⁴.
As a result, every hexadecimal digit corresponds exactly to four binary bits. This means hex can be converted to binary directly, one digit at a time, without first converting the full value to decimal.
Hexadecimal — Base 16
Uses digits 0–9 and A–F, with each digit representing four binary bits.
Binary — Base 2
Uses only 0 and 1 and represents digital values directly as bits.
How to Use the Hex to Binary Converter
Type a value such as 2F. Valid characters are 0–9 and A–F.
Lowercase a–f is also accepted.
BinaryCon maps every hexadecimal digit to an exact 4-bit binary group.
The 4-bit groups are joined in their original order to form the complete binary representation.
The main result removes only insignificant zeros at the far left while the breakdown preserves complete 4-bit groups.
Use the result for programming, bitwise work, electronics, debugging, coursework, or another BinaryCon tool.
Hexadecimal to Binary Conversion Table
The complete hex-to-binary mapping contains only sixteen entries. Memorizing this table makes manual conversion very fast.
| Hex Digit | Decimal | 4-Bit Binary |
|---|---|---|
| 0 | 0 | 0000 |
| 1 | 1 | 0001 |
| 2 | 2 | 0010 |
| 3 | 3 | 0011 |
| 4 | 4 | 0100 |
| 5 | 5 | 0101 |
| 6 | 6 | 0110 |
| 7 | 7 | 0111 |
| 8 | 8 | 1000 |
| 9 | 9 | 1001 |
| A | 10 | 1010 |
| B | 11 | 1011 |
| C | 12 | 1100 |
| D | 13 | 1101 |
| E | 14 | 1110 |
| F | 15 | 1111 |
Worked Example: Convert Hex 2F to Binary
Hexadecimal 2F contains two digits: 2 and F.
Example: Convert Hex FF to Binary
F → 1111 Join the groups: FF₁₆ → 1111 1111₂ Therefore: FF₁₆ = 11111111₂ Both values equal decimal 255.
Example: Convert Hex 1A3 to Binary
A → 1010
3 → 0011 Join the groups: 0001 1010 0011 Remove insignificant zeros from the far left: 110100011 Therefore: 1A3₁₆ = 110100011₂
Hex to Binary Reference Examples
| Hex | Binary | Decimal |
|---|---|---|
0 | 0 | 0 |
1 | 1 | 1 |
A | 1010 | 10 |
F | 1111 | 15 |
10 | 10000 | 16 |
1F | 11111 | 31 |
20 | 100000 | 32 |
2D | 101101 | 45 |
3F | 111111 | 63 |
40 | 1000000 | 64 |
7F | 1111111 | 127 |
80 | 10000000 | 128 |
FF | 11111111 | 255 |
100 | 100000000 | 256 |
1FF | 111111111 | 511 |
FFF | 111111111111 | 4095 |
Why One Hex Digit Equals Four Binary Bits
Four binary bits can form sixteen unique combinations:
from 0000 through 1111.
Hexadecimal also needs exactly sixteen digit values: 0 through 9 and A through F.
This exact mathematical relationship creates a one-to-one mapping between every hexadecimal digit and one four-bit binary group.
What Happens to Leading Zeros?
Each hex digit should first be mapped to all four binary bits, even when that group begins with zeros.
For example:
2 → 0010
F → 1111
Grouped binary = 0010 1111
If the goal is the ordinary unsigned numeric representation, the zeros at the far left can be removed:
Do not remove zeros from inside the binary number because that would change its place values and therefore the number itself.
Hex Bytes and Binary Bits
Two hexadecimal digits represent exactly eight binary bits, which is one byte. This makes hexadecimal especially convenient for byte-oriented computing.
| Hex Digits | Binary Bits | Common Description |
|---|---|---|
| 1 | 4 | Nibble |
| 2 | 8 | Byte |
| 4 | 16 | 16-bit value |
| 8 | 32 | 32-bit value |
| 16 | 64 | 64-bit value |
Why Hex FF Equals Binary 11111111
Hexadecimal F has decimal value 15 and maps to binary
1111.
Therefore two F digits produce:
F → 1111
FF → 11111111
Eight 1 bits represent decimal 255, the maximum unsigned value of one byte.
Hex, Binary, and Decimal Comparison
| Hex | Binary | Decimal |
|---|---|---|
| A | 1010 | 10 |
| B | 1011 | 11 |
| C | 1100 | 12 |
| D | 1101 | 13 |
| E | 1110 | 14 |
| F | 1111 | 15 |
| 10 | 10000 | 16 |
| FF | 11111111 | 255 |
Why Hexadecimal Is Popular in Computing
Binary accurately represents machine-level data, but long binary strings can be difficult for people to scan. Hexadecimal compresses every four bits into one character while keeping exact bit boundaries.
Hex: FFA3
The shorter hexadecimal form is easier to read, copy, compare, and debug, while each character can still be expanded directly back to four bits.
Where Hex to Binary Conversion Is Useful
Programming
Developers convert hex to binary to inspect masks, flags, register fields, protocol values, and bit-level structures.
Debugging
Hex dumps and debugger values can be expanded to binary when individual bits or fields must be inspected.
Digital electronics
Hex notation is often used for registers and bus values, while binary reveals the individual digital states.
Computer science education
Direct 4-bit mapping is a useful way to understand the mathematical relationship between base 16 and base 2.
Common Hex to Binary Conversion Mistakes
During mapping, always use a complete 4-bit group. Hex 2 maps to
0010, not merely 10.
A=10, B=11, C=12, D=13, E=14, and F=15.
Only insignificant zeros at the far left of the complete unsigned value may be removed.
Three bits correspond to octal digits. Hexadecimal requires four bits per digit.
Related BinaryCon Tools
Reverse this conversion or continue from hexadecimal into decimal, octal, ASCII, and other formats.
Hex to Binary Converter FAQs
How do you convert hexadecimal to binary?
Replace each hexadecimal digit with its corresponding four-bit binary group and join the groups in the same order. For a normal unsigned numeric result, insignificant zeros at the far left can then be removed.
What is hex A in binary?
Hexadecimal A represents decimal 10 and maps directly to binary 1010.
What is hex F in binary?
Hexadecimal F represents decimal 15 and maps to 1111.
What is hex 2F in binary?
Hex digit 2 maps to 0010 and F maps to
1111. Together they produce 00101111,
or 101111 after removing insignificant leading zeros.
What is FF in binary?
Each F maps to 1111, so hexadecimal FF becomes
11111111 in binary.
What is hex 1A3 in binary?
Map the digits as 1 → 0001, A → 1010, and 3 → 0011.
The grouped result is 000110100011, or
110100011 as the significant unsigned binary value.
Why does every hex digit use four binary bits?
Four bits provide 2⁴ = 16 possible patterns, exactly matching the sixteen digit values used in hexadecimal.
Can hexadecimal letters be lowercase?
Yes. Hex values are case-insensitive in normal numeric notation.
FF, ff, and Ff have the same
value. BinaryCon accepts lowercase and normalizes it internally.
Does 0x change the hexadecimal value?
No. In programming, 0x is commonly a prefix indicating that
the following digits are hexadecimal. It is not one of the actual digits.
This calculator expects the hexadecimal digits themselves.
Why does FF equal 11111111?
Each F equals binary 1111. Two F digits therefore create two four-bit groups: 1111 1111, which is the eight-bit value 11111111.
Can this converter handle very long hexadecimal strings?
Yes. Conversion is performed directly using character-to-bit mapping instead of converting the complete input into a floating-point number. This avoids ordinary integer precision issues for long hex strings.
Is hex-to-binary conversion exact?
Yes. Each hexadecimal digit has one exact four-bit equivalent, so integer conversion does not require approximation or rounding.
What is one byte in hexadecimal and binary?
One byte contains eight bits and can therefore be represented by exactly two hexadecimal digits. For example, hexadecimal FF corresponds to binary 11111111 and decimal 255.
Convert Hex to Binary Instantly
Use BinaryCon for exact hexadecimal-to-binary conversion, 4-bit mapping, grouped results, verified examples, reference tables, and free number-system tools without registration.