Hex to Binary Converter

Going the other way? Convert binary back to hex →

How do you convert hex to binary?

Hex to binary conversion works in groups of 4 bits, because one hexadecimal digit is worth exactly 4 bits, so no arithmetic is needed.

1. Take the first hexadecimal digit.
2. Write it as 4 binary digits from the table.
3. Repeat for every digit, keeping the order.
4. Join the groups and drop any leading zeros: 2F = 101111.

Hexadecimal to Binary Conversion Table

One hexadecimal digit equals exactly 4 bits (16 = 2⁴); one octal digit equals exactly 3 bits (8 = 2³). Hex and octal are therefore converted by grouping bits, and hex ↔ octal passes through binary. That is the whole method, so the table below is the only thing you need: every group of 4 bits has exactly one hex digit, and the mapping never changes. Binary writes values on the digit set 0, 1 with each place worth 2ⁿ, and a value marked 0b is binary; hex values are marked 0x.

Each base is defined by three things: which digits it uses, how a value is marked, and what each position is worth.

Worked Example: 2F to Binary

One value, converted the long way so the working is visible. This is the same grid the converter shows when you turn on "show steps".

Both bases here are powers of two, so no division is needed. One hexadecimal digit is worth exactly 4 bits, which means the conversion is a regrouping of the same bits rather than a change of value.

Written out, 2F is 101111 in binary. Regrouping those bits into 4s from the right, and padding the leftmost group with zeros if it is short, gives 101111. Counting the groups from the left instead is where this goes wrong: the padding then lands on the wrong end and every digit shifts.

Check it in reverse

The value returns unchanged. Convert 101111 back and you get 2F, because a base change rewrites the digits without touching the quantity they stand for. That is the whole test: if the round trip differs, a digit was misread. To check it by hand, convert the hex value back to binary and compare it with the number you started from.

Worked examples: hex to binary

Each example gives the value first, then the working. Click a value to load it in the converter.

Every example above reverses exactly — regroup the same bits into hex digits.

What About Padding, Fractions and Width?

Leading zeros and width

A number carries no leading zeros unless a width is fixed. 101111 and 0101111 are the same value, so the converter writes the short form. Fixed widths belong to bytes and registers, not to arithmetic. repeated division and positional expansion covers where width does matter.

Fractions and the point

Digits after a point convert by the same rule with negative powers, so the first place after the point is worth 1/2. Many fractions that end neatly in decimal repeat forever in binary, which is where rounding creeps in.

Negative values

A minus sign is kept in front of the digits. Fixed-width binary encodes sign differently, using two's complement, and that is a separate rule from the base change itself.

How large a value can be

The method has no ceiling; each extra hexadecimal digit multiplies the range by 16. Practical limits come from the width a machine stores the value in, not from the conversion.

Hex to Binary in Code

The same rule in one line. Both group the bits and return the binary digits.

Python: format(int('2F', 16), 'b')

JavaScript: parseInt('2F', 16).toString(2)

Common Mistakes

• Reading the remainders top to bottom. They come out in reverse, so the digits land backwards.
• Using a digit the base does not have — an 8 in octal, or a 2 in binary. The value cannot be read at all.
• Grouping bits from the left. Groups are counted from the right, and the leftmost group is the one that gets padded.
• Treating the result as a character code. 41 is a number here, not the letter A.

Frequently Asked Questions

Related Conversions

• Hexadecimal also converts to decimal by the same route — hex to decimal by positional expansion.
• Hexadecimal also converts to ascii by the same route — hex byte to ASCII code lookup (00-7F).
• Hexadecimal also converts to octal by the same route — hexadecimal to octal calculator with the working.
• If your input is text rather than hexadecimal, write your name in binary (8 bits per character) instead.
• If your input is decimal rather than hexadecimal, convert decimal to binary instead.
• If your input is binary rather than hexadecimal, add up the place values of a binary number instead.

The rest of the family sits on binary, octal, decimal and hex converters.