Beetwise

Convert octal to binary

One octal digit holds exactly three bits.

To convert octal to binary, replace each digit with its three bits.

To convert binary to octal, split the bits into groups of three from the right.

Try octal to binary conversion in the bit editor

The octal value 454 as bits. Edit the expression or select a bit to flip it.

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0b0000000100101100
binary · 16 bits
octal
0o454

Octal to binary conversion step by step

Replace each octal digit with its three bits: The steps follow the value above.

  1. Write the value as bits: 000000000100101100
  2. Split the bits into groups of three, from the right: 000 000 000 100 101 100
  3. The group 000 is the octal digit 0.
  4. The group 000 is the octal digit 0.
  5. The group 000 is the octal digit 0.
  6. The group 100 is the octal digit 4.
  7. The group 101 is the octal digit 5.
  8. The group 100 is the octal digit 4.
  9. The result is 0o000454.

Every octal digit as three bits

Every octal digit as three bits
OctalBinaryDecimal
00000
10011
20102
30113
41004
51015
61106
71117

Where octal to binary conversion is used

A permission of 755 becomes 111 101 101, one group for each group of three bits.

A field of three bits in a register reads as one octal digit.

The conversion needs no arithmetic, so it works by eye.

Octal to binary conversion: points to note

  • Group the bits from the right. A short group at the left needs zeros in front.
  • An 8-bit register does not divide into whole octal digits, because 8 is not a multiple of 3.
  • Hex needs no extra zeros for a byte, which is why a register view uses hex.
  • Do not mix the prefixes. The value 0o10 is 8 and the value 0b10 is 2.

The full bit editor

The full editor holds many values, evaluates expressions across them, and reads live values from a serial port.

Open this value in the full editor

Questions about octal to binary conversion

How many bits does one octal digit hold?
One octal digit holds three bits, because eight values need three bits.
What is 0o755 in binary?
The octal value 755 is 111101101. Each digit gives three bits.
Why does hex suit a byte better than octal?
A byte is two groups of four bits, so two hex digits cover it. Three does not divide eight.