Hex to Binary Converter

What the hex to binary converter does

This does the opposite of compressing binary into hex. It takes a hex value and expands it back into the full string of 0s and 1s underneath. Type the hex in, press the button, and copy out the binary.

It is what you want when you need to see the actual bits, not the tidy hex shorthand, because some jobs only make sense at the level of individual 0s and 1s.

How to use it

1. Enter your hex number. Use digits 0 to 9 and letters A to F, entered as capitals.
2. Press Convert. The binary version appears in the output box.
3. Click the result to copy it. Tap the output to copy it to your clipboard.

Press Reset to clear both boxes.

Each hex digit is four bits

The same friendship between hex and binary makes this direction easy too. Because one hex digit covers the values 0 to 15, it maps onto exactly four bits. So you do not work on the number as a whole. You take each hex digit on its own, write down its four-bit pattern, and string all the pieces together in order. One hex digit in, four bits out.

A worked example with real numbers

Take the hex number 3C. Handle each digit separately.

• 3 is 0011 in four bits.
• C is 12, which is 1100 in four bits.

String them together in the same order: 00111100. So 3C in hex is 00111100 in binary. Each digit simply unfolded into its own four bits.

The sixteen patterns

There are only sixteen four-bit patterns to know, one per hex digit, and they are worth a glance because they make this conversion instant.

Each hex digit always becomes a full four bits, including its leading zeros, so 3 expands to 0011, not just 11. That is what keeps the pieces lined up when you join them.

Why blow hex back up into bits

Hex is lovely for reading and writing, but a lot of real work happens bit by bit. If you are setting or clearing a single flag, applying a mask, or working out what a bitwise operation will do, you need the individual bits in front of you, not a hex digit standing in for four of them at once. Expanding the hex first lets you see exactly which switches are on and which are off.

Questions people ask

How do I convert hex to binary by hand?

Take each hex digit on its own, write its four-bit pattern, and join the patterns in order. There is no arithmetic across the whole number.

Do I keep the leading zeros in each group?

Yes, within each digit. Every hex digit becomes a full four bits, so 5 is 0101 and 1 is 0001. Keeping all four keeps the pieces aligned when you string them together.

Why does each hex digit give four bits?

Because a hex digit ranges over 0 to 15, and four bits cover exactly that range, so one digit fits neatly into four bits with nothing left over.

Should I type the letters as capitals?

Yes, enter A to F as capitals, which is the usual way hex digits are written.

References

1. Weisstein, Eric W. "Binary." From MathWorld, A Wolfram Resource. https://mathworld.wolfram.com/Binary.html