Binary to Hexadecimal Converter

Why four bits make one hex digit

Hexadecimal is base 16, and 16 is 2 to the fourth power. That is the entire reason the conversion is easy. Four binary digits produce exactly sixteen possible patterns — 0000 through 1111 — and hex has exactly sixteen digits, 0 through 9 then A through F. The mapping is one-to-one with nothing left over.

So converting binary to hexadecimal never involves arithmetic. You are not calculating anything; you are relabelling. Chop the bits into fours, look each group up, write the character down. Converting binary to decimal is genuinely harder, because ten is not a power of two and the conversion needs real division. This is why hex, not decimal, is what you see whenever anyone is working close to the machine.

A four-bit group has a name: a nibble. Two nibbles make a byte, which is why a byte is always exactly two hex digits, and why hex is the natural way to write raw data. A 32-bit value that would sprawl across thirty-two ones and zeros collapses into eight characters you can read at a glance and say out loud.

How to convert binary to hexadecimal, step by step

1. Start from the rightmost bit — the one nearest the point, not the leftmost.
2. Split the digits into groups of four, working right to left.
3. If the leftmost group comes up short, pad it on the left with zeros until it has four digits. Leading zeros never change the value.
4. Convert each 4-bit group to its hex digit using the nibble table above.
5. Write the digits in the same left-to-right order as their groups.

Direction is where people go wrong. Grouping from the left instead of the right produces a wrong answer any time the bit count is not already a multiple of four. Binary 101101 grouped from the left gives 1011 and 01, which reads as B1 — but grouped correctly from the right it gives 0010 and 1101, which is 2D. Check it in decimal: 101101 is 45, and 2D is (2 x 16) + 13 = 45. B1 would be 177, which is nowhere close.

Worked examples

Converting hexadecimal back to binary

The reverse direction is easier because there is no padding decision. Replace each hex digit with its four binary digits, keep the order, then drop any leading zeros at the very end. Hex 2D becomes 0010 and 1101, which reads 00101101, which is 101101 once the leading zeros go.

The rule people forget is that every digit expands to exactly four bits, including small ones. Hex 5 is 0101, and in the middle of a number it must stay as the full 0101. Hex 41 is 01000001, not 1000001. Only the leading zeros of the whole result get dropped, never the ones inside. Use the swap button on the converter to go this direction without retyping.

Nibbles, bytes and why hex won

A nibble is four bits and a byte is eight, so a byte is always exactly two hex digits — never one, never three. That fixed relationship is why hex became the standard way to write raw data and why octal, which groups in threes, largely fell out of use. Three does not divide eight, so a byte in octal takes an awkward three digits with the top one only partly used. Four divides eight perfectly.

This is worth internalising because it makes hex readable at a glance. Every pair of characters is one byte. A four-character hex value is two bytes, or a 16-bit word. Eight characters is four bytes, a 32-bit value. When you see an address like 0x7FFF5FBF you can immediately count four bytes without doing any arithmetic. Set the grouping control on the converter above to Byte and the visualiser will draw those boundaries for you.

Binary fractions and the point

Bits after a binary point convert just as cleanly, but the padding direction reverses. Before the point you pad on the left; after it you pad on the right. Place values radiate outward from the point in both directions, so the group nearest the point is the one that must stay complete.

Take 0.11. Two fractional bits, so pad right to 0.1100, which is one nibble: 1100, or hex C. So 0.11 binary is 0.C hex. Check it: 0.11 binary is 0.75, and C is 12, and 12/16 is 0.75. Now 1010.11 — the integer part 1010 is one complete nibble giving A, and the fractional part pads to 1100 giving C, so the answer is A.C. None of the pages ranking for this term accept a binary point at all.

Where you'll meet binary and hex together

Hex exists to make binary readable, so the two almost always turn up in the same places. Knowing which one you are looking at, and being able to move between them, is most of the skill.

Who uses this and why