Number Converters · Browser · Free

Octal to Binary Converter

Type an octal number and read off its binary form, with the decimal and hexadecimal forms next to it. Nothing is worked out until you press Convert.

What octal and binary mean

Octal is base 8, so it spells numbers with the digits 0 to 7. Every place stands for a group eight times as large as the place on its right, so after the ones place comes eights, then groups of eight eights, and so on.

Binary is base 2 and spells numbers with the digits 0 and 1 only. Its places double from one to the next instead of growing by eights, which is why the same amount takes more digits to write out in binary than in octal.

Octal to binary formula

The idea is to read the octal number place by place and then write that same amount with binary places. The row 17 octal = 1111 binary in the table is exactly that: the octal side holds one eight together with seven ones, and the binary side spreads the same amount over four doubling places.

Longer rows work the same way and can be checked against the table one place at a time. The table gives 144 octal as 1100100 binary, 377 octal as 11111111 binary, and 2000 octal as 10000000000 binary.

Using this converter

There is one text field. A sign and a fractional point are both accepted, and several numbers separated by spaces are converted one by one rather than read as a single value.

The answer appears in a card below the button, and the card carries the decimal and hexadecimal forms alongside the binary one, with any letters printed in uppercase. Copy writes the result and its unit to the clipboard, and Clear resets the form.