How to Convert Hex to Binary (Step by Step, With Worked Examples)

Hexadecimal and binary are two ways of writing the same numbers. Binary is what computers actually use, but it gets long and hard to read fast. Hex is the compact shorthand programmers use instead — and converting between them is one of the easiest conversions in computing, once you know the one simple rule behind it.

The One Rule You Need

Every hex digit is exactly 4 binary bits.

That is the whole trick. A hex digit can hold 16 different values (0–15), and 4 binary bits can also hold exactly 16 values (0000–1111). So you never have to convert the whole number at once — you just swap each hex digit for its 4-bit group, one digit at a time, and join the groups together.

This is also why hex and binary pair up so neatly, and why the reverse conversion works the same way — if you have done binary to hex before, this will feel familiar, just in the opposite direction.

Hex Digit to Binary Table (0–F)

Keep this table next to you while you practise:

Notice the pattern at the top: 0–9 in hex match the numbers 0–9, and their binary is just that number written in 4 bits. The letters A–F simply continue from 10 to 15.

How to Convert Hex to Binary: Step by Step

1. Write down each hex digit separately.
2. Replace every digit with its 4-bit binary group from the table. Always write all 4 bits, including leading zeros.
3. Join the groups together in the same order. That is your binary number.

Example 1: 2F

• 2 → 0010
• F → 1111
• Joined: 0010 1111, which is written as 101111

Example 2: A3

• A → 1010
• 3 → 0011
• Joined: 1010 0011

Example 3: FF

• F → 1111
• F → 1111
• Joined: 1111 1111

Example 4: 1C4

• 1 → 0001
• C → 1100
• 4 → 0100
• Joined: 0001 1100 0100, written as 111000100

That is genuinely all there is to it. A longer example, DE, works the same way: D → 1101 and E → 1110, giving 1101 1110.

How to Check Your Answer

The safest check is to convert your answer back to hex. Take your binary result and split it into groups of 4 bits, starting from the right. Convert each group back into a hex digit. If you get your original number, your answer is right.

Check Example 4: 111000100 splits from the right into 0001 | 1100 | 0100, which is 1, C, 4 — back to 1C4. Correct.

You can also sanity-check with decimal if you know the value: 2F is 47 in decimal, and 101111 is also 47. If you want to practise that side of things, see our guide on how to convert binary to decimal.

Common Mistakes to Avoid

Dropping leading zeros inside groups. This is the number one error. In A3, the 3 must be written as 0011, not 11. If you drop the zeros, you get 101011 — a completely different number — and the groups no longer line up when you check your work. The only zeros you may drop are the ones at the very front of the finished answer (0010 1111 can be written as 101111).

Reading the groups in the wrong order. The first hex digit is always the leftmost group. Reversing them changes the number entirely.

Trying to convert the whole number through decimal. It works, but it is slow and error-prone. Digit-by-digit is faster and almost impossible to get wrong once the table is familiar.

Why Is Hex Used at All?

If computers think in binary, why bother with hex? Because binary numbers get huge fast — a single byte is 8 bits, and memory addresses can be 64 bits long. Hex shrinks every 4 bits into one character, so the same value takes a quarter of the space and is far easier to read, copy, and compare.

You will meet hex in everyday places:

• Colors on the web: a color like #FF5733 is three hex pairs — one each for red, green, and blue.
• Memory addresses and error codes: programmers read values in hex because binary would be unreadably long.
• MAC addresses: a network device’s hardware address (such as 00:1A:2B:3C:4D:5E) is written in hex pairs.

In every case, hex is just binary in a friendlier outfit — which is why the 4-bit rule works.

Convert Hex and Binary Instantly

Doing a few conversions by hand is the best way to learn, but for long values let a tool do the grouping. Our free Binary Translator converts between text, binary, and related formats instantly — paste your value in and check your manual answer in seconds.

Frequently Asked Questions

How do I convert hex to binary quickly?

Replace each hex digit with its 4-bit binary group from the 0–F table, then join the groups in order. For example, 2F becomes 0010 1111.

Why does each hex digit equal exactly 4 bits?

Because both can represent exactly 16 values. Four bits give 2⁴ = 16 combinations (0000 to 1111), and a hex digit also has 16 possible values (0 to F), so they match up perfectly.

Can I drop the zeros in each group?

Only the leading zeros of the whole finished number. Zeros inside the number — including the leading zeros of each 4-bit group — must stay, or the value changes.

What is FF in binary?

FF is 1111 1111 — eight 1s, which is one full byte with every bit switched on. In decimal, FF is 255.

Is hex to binary the same as binary to hex in reverse?

Yes. Converting binary to hex groups binary into sets of 4 bits and swaps each group for a hex digit; hex to binary simply runs the same table backwards, digit by digit.