Binary to Hex Converter

What the binary to hex converter does

Long binary is hard on human eyes. A row of sixteen or thirty-two 0s and 1s is almost impossible to read without losing your place. This tool turns that binary into hexadecimal, the short, tidy base-16 form. Type the binary in, press the button, and copy out the hex.

The two get along unusually well, and converting between them needs no real arithmetic, just a little grouping, which is the nice part.

How to use it

1. Enter your binary number. Type the 0s and 1s, for example 11011110.
2. Press Convert. The hex version appears in the output box.
3. Click the result to copy it. Tap the output to send it to your clipboard.

Press Reset to clear both boxes.

The four-bit trick

Here is why binary and hex are such good friends. Sixteen is two to the fourth power, which means a group of exactly four bits can count from 0 to 15, the same range as a single hex digit. So you do not convert the whole binary number at once. You split it into groups of four bits, starting from the right, and turn each group into its own hex digit. Four bits in, one hex digit out, every time.

A worked example with real numbers

Take the binary number 11011110. Split it into fours from the right, which gives two clean groups.

• 1101 on the left. That is 8 + 4 + 1 = 13, which in hex is D.
• 1110 on the right. That is 8 + 4 + 2 = 14, which in hex is E.

Put the hex digits in the same order as the groups: DE. So 11011110 in binary is DE in hex. Notice you never had to deal with the whole eight-bit number, only two small four-bit pieces.

When the bits do not divide by four

Often the number of bits is not a clean multiple of four. No problem: you pad the leftmost group with 0s until it is four bits wide. Leading zeros never change a number's value, so this is always safe.

Take 110111, which is only six bits. Group from the right and the left group is short, so pad it: 0011 and 0111. That is 3 and 7, giving 37. And sure enough, 110111 in binary and 37 in hex are both 55 in decimal.

Why this is so handy

The grouping lines up perfectly with how computers store data. A byte is eight bits, and eight bits is exactly two groups of four, so every byte is exactly two hex digits, running from 00 to FF. That is why a hex dump of memory shows two neat hex characters per byte instead of eight scattered bits. Hex gives you all the information of the binary in a quarter of the width, with no loss and no rounding.

Questions people ask

How do I convert binary to hex by hand?

Split the binary into groups of four bits starting from the right, pad the leftmost group with leading zeros if needed, then turn each four-bit group into its single hex digit and keep them in order.

What if the number of bits is not a multiple of four?

Pad the leftmost group with 0s on the left until it has four bits. Leading zeros do not change the value, so the answer stays correct.

Why four bits per hex digit?

Because sixteen is two to the fourth, so four bits cover exactly the values 0 to 15, which is the full range of one hex digit.

How many hex digits is one byte?

Two. A byte is eight bits, which splits into two groups of four, so every byte is two hex digits, from 00 to FF.

References

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