Welcome to our Hexadecimal to Binary Converter, a free online tool built around one of the neatest ways to represent binary data. If you observe a bit more carefully, sixteen is exactly two raised to the fourth power. It is thus the relationship between these two number systems that makes converting from one to another easy.

Hexadecimal, or base 16, is the compact shorthand that humans use to read machine data: it squeezes a row of bits into a short string built from the digits 0 to 9 and the letters A to F. Binary is the raw language of the hardware itself, a stream of 0s and 1s that circuits can switch on and off.
This tool acts as the bridge between the number systems and gives accurate and instant conversions.

It is a favorite among students learning how number systems relate, and it is equally at home in serious work: checking bit masks, decoding protocol fields, verifying register dumps, or peeking at machine code. Integer or fractional, uppercase or lowercase, the converter turns your hex input into binary in a single click.

Hexadecimal Number System

The hexadecimal number system, or base 16, stands in for four binary bits at a time. It needs sixteen symbols to do that: the digits 0 to 9 for the values zero through nine, and the letters A to F for the values ten through fifteen. Because each position is a power of 16, the digits climb in value much faster than in decimal, which is why compact strings like FF can describe an entire byte of data.

Consider the hexadecimal number "5B" and how it unpacks into binary:

1. The rightmost digit (B) , which stands for the value 11, is the binary equivalent of 1011.
2. The leftmost digit (5) , which stands for the value 5, is the binary nibble 0101.

Join the two parts together to get 0101 1011, then drop the leading zero to leave 1011011.

Therefore, the hexadecimal number (5B)₁₆ is equivalent to the binary value (1011011)₂, which itself equals the decimal value (91)₁₀.

Hexadecimal numbers can carry a fractional part too. Take 2F.4, for an example. The integer part 2F in binary will be (2 → 0010, F → 1111), which combine to 00101111 and then simplify to 101111. The fractional digit .4 works with negative powers of 16, specifically 16^-1, or one sixteenth - giving 4 × 1/16 = 0.25, which is written as .01 in binary. The converter reports the full result as 101111.01.

Therefore, the hexadecimal number (2F.4)₁₆ is equivalent to the binary value (101111.01)₂.

Binary Number System

The binary number system, or base 2, is the language of the machine. It uses only two symbols, 0 and 1, which map neatly onto the two states of a circuit: off and on. Each position in a binary number is a power of two, starting at 2⁰ on the right and doubling as you move left. The binary number "110101" can be read like this:

1. The rightmost digit (1) is in the one's place, (1 * 1 = 1)
2. The next digit (0) is in the two's place, (0 * 2 = 0)
3. The next digit (1) is in the four's place, (1 * 4 = 4)
4. The next digit (0) is in the eight's place, (0 * 8 = 0)
5. The next digit (1) is in the sixteen's place, (1 * 16 = 16)
6. The leftmost digit (1) is in the thirty-two's place, (1 * 32 = 32)

Adding those together, (1 + 0 + 4 + 0 + 16 + 32) = (53)₁₀, which is written as (35)₁₆ in hexadecimal.

The key idea that makes this whole page possible is a simple one: since 16 = 2⁴, each hexadecimal digit always corresponds to exactly four binary bits. Learn those sixteen four-bit patterns and you can read binary written in hex almost as easily as you read text.

Our Hexadecimal to Binary Converter takes the pain out of converting a hexadecimal value to its equivalent binary representation in no time and with precision.

Just type or paste a hexadecimal number (also called a hex number) and press "Convert to Binary" to see its binary equivalent immediately. Prefer to see everything at once? Hit "Convert to All" and the tool fills in the decimal and octal forms of the same value right beside the binary result. It is perfect for cross-checking your work.

You can also copy the binary output straight to your clipboard, wipe the fields with the clear option, or save the full conversion set as a text file for your notes. There is nothing to install and nothing to sign up for, so it is ready whenever you need to see what a hex value really looks like in raw bits.

At a Glance:

For an integer hexadecimal number (no decimal point), replace each hexadecimal digit with its four-bit binary representation and put the parts together in order. Any leading zeros that end up at the front of the result can be dropped.

For a fractional hexadecimal number (with a decimal point), split it at the point first. Convert the integer part using the same above method, then handle each fractional digit with a negative power of 16, e.g the first digit after the point is in the 16^-1 place, the second in the 16^-2 place, and so on. Finally, join the integer and fractional parts around the decimal point.

In Detail:

Manual conversion is fast once you have the sixteen nibble patterns memorized. Here are the steps, using A3F.8 as our example:

Step 1: Separate the number into integer and fractional parts, if it has a decimal point. A3F.8 splits into the integer A3F and the fraction .8.

Step 2 (For the Integer Part): Look up each hex digit in the nibble table below and write down its four-bit group, keeping the original order.

Hex Digit	Decimal Value	Binary Nibble
A	10	1010
3	3	0011
F	15	1111
.	.	.
8	8	1000

Step 3 (For the Integer Part): Concatenate the integer nibbles. A → 1010, 3 → 0011 and F → 1111 give 1010 0011 1111, which is 101000111111 once written as a single string.

Step 4 (For the Fractional Part): Read the fraction digit with a negative power of 16. The digit 8 sits in the 16^-1 place, so its value is 8 × 0.0625 = 0.5, which is 0.1 in binary (the trailing zeros of the nibble are simply not shown).

Step 5: Combine the two halves.

Therefore, the hexadecimal number (A3F.8)₁₆ is equivalent to the binary value (101000111111.1)₂.

If you ever forget a nibble, the positional method still works: multiply each hex digit by the appropriate power of 16 to get its decimal value, convert that to binary, and sum the results. The nibble trick is simply the shortcut that makes it feel effortless.

Example 1: Hexadecimal to Binary Conversion: 1A.
To convert the hexadecimal number 1A into binary, follow these steps:

Step 1: Look up each hex digit in the nibble table: 1 → 0001 and A → 1010.
Step 2: Join the nibbles: 0001 1010.
Step 3: Drop the leading zeros: 00011010 → 11010. Thus, the binary equivalent of (1A)₁₆ is (11010)₂.

Example 2: Hexadecimal to Binary Conversion: 3F.C.
To convert the hexadecimal number 3F.C into binary, follow these steps:

Step 1: Separate the integer and fractional parts: Integer 3F and Fractional .C.
Integer Part (3F):
Step 2: Convert each digit to its nibble: 3 → 0011 and F → 1111.
Step 3: Join and trim: 00111111 → 111111.
Fractional Part (C):
Step 4: The digit C (12) sits in the 16^-1 place, so 12 × 0.0625 = 0.75, which is .11 in binary. Combining the two halves, the binary equivalent of (3F.C)₁₆ is (111111.11)₂.

Example 3: Hexadecimal to Binary Conversion: FFA.
To convert the hexadecimal number FFA into binary, follow these steps:

Step 1: Convert each digit to its nibble: F → 1111, F → 1111, and A → 1010.
Step 2: Join the nibbles: 1111 1111 1010.
Step 3: The result already starts with a 1, so no trimming is needed: 111111111010. Therefore, the binary equivalent of (FFA)₁₆ is (111111111010)₂.

There are plenty of ways to flip between number systems, so here is why this converter is worth keeping in your bookmarks:

Effortless Conversion:

No need to memorize the sixteen nibble patterns or work out powers of 16 by hand. Type your hex value and the binary result appears instantly.

No Sign-Up Required:

There is no account, no registration, and no login wall. Open the page, convert, and close it again without handing over any personal details.

Quick Results:

The conversion runs in your browser, so there is no waiting on a server. Results are effectively immediate, even for long strings of digits.

Accurate and Reliable:

The converter applies standard positional math to every input, so you can trust the output when you are double-checking bit patterns or verifying your own work.

Cross-Platform Compatibility:

It works in any modern browser on desktop and mobile alike: be it Windows, macOS, Linux, iOS, or Android - with no plugins to install.

Absolutely Free:

Every feature, including Convert to All and the download option, is available at no cost. No trial periods, no hidden fees, no subscriptions.

Handles Long Values with Ease:

Whether it is a two-digit hex value or a long chain of digits, the tool converts without breaking a sweat. Results are exact for values up to about 14 hex digits (roughly 9 quadrillion); for extremely long values, JavaScript number precision may round the final digits.

FAQ 1: Is this tool free to use?
Answer: Yes, completely. You can use it as often as you like, with no registration, subscription, or payment of any kind.

FAQ 2: Why does each hexadecimal digit translate to exactly four bits?
Answer: Because 16 is 2 raised to the fourth power. Four binary bits can express 16 different combinations (0000 to 1111), which is exactly the number of symbols hexadecimal uses.

FAQ 3: Does the tool accept lowercase letters?
Answer: Yes. Inputs like ff and 1a are handled the same way as their uppercase forms.

FAQ 4: Can it convert fractional hexadecimal values like 2F.4?
Answer: Yes. Fractional parts are converted using negative powers of 16, so 2F.4 comes back as 101111.01.

FAQ 5: Why do the leading zeros disappear from the output?
Answer: Binary numbers are normally written without leading zeros, just as you would not write the decimal number 26 as 0026. So 1A becomes 11010 rather than 00011010, even though both mean the same thing.

FAQ 6: When would I actually need a hex to binary conversion?
Answer: It comes up whenever you need to see the individual bits behind a value: checking bit masks, decoding protocol headers, reading register dumps, or reviewing machine code that is conventionally shown in hex.