Number Converters · Browser · Free

Hex to Binary Converter

Type a hexadecimal number and the converter writes it out in binary, and also in decimal and octal. A leading sign and a fractional point are accepted, and several numbers separated by spaces are converted one by one.

What this tool converts

The tool takes a hexadecimal number, which is base 16, and writes the same amount as a binary number, which is base 2. The decimal and octal forms of the value are shown alongside it, so a single entry gives you the binary, decimal and octal reading of the number together. Everything is entered in one text field.

A leading sign and a fractional point are accepted. If you put several numbers in the field separated by spaces, each one is converted separately. Letters in the result print in uppercase.

The form computes only when you press Convert, and the result appears in a card below the button. Copy writes the result and its unit to the clipboard, and Clear resets the form to empty. It all runs in the browser, so nothing is uploaded.

Hex to binary formula

Hexadecimal is base 16 and binary is base 2, and in both of them the place a digit sits in decides what that digit is worth. In hexadecimal each place is worth sixteen times the place to its right; in binary each place is worth twice the place to its right. A conversion simply spreads one amount over those places twice, once in each base.

The row 1F = 11111 in the table shows the method. On the hexadecimal side the 1 sits one place left of F, so it counts in units of sixteen while F fills the place at the right. On the binary side five digits cover places that double one after another, the leftmost being the sixteen place. Both strings of digits stand for the same amount, which is why they are listed together.

The row 64 = 1100100 is the same idea with some places left empty: those zeros mark places that carry nothing. Rows such as 8 = 1000 and 100 = 100000000 show the places at either end of a run, FF = 11111111 shows every binary place filled for two hexadecimal digits, and 0 = 0 shows the amount that leaves all of them empty.