18 min read

Binary and Octal

One octal digit is exactly three bits. Group bits in threes from the right — padding with leading zeros — to convert quickly.

Why Groups of Three?

8 = 2³. So every octal digit (0-7) can be written as exactly three bits, from 000 to 111. This makes binary \leftrightarrow octal conversion fast — no division needed.

Each group uses the place values 4, 2, 1.

1 Split the bits into groups of three, starting from the right . 2 If the left-most group has fewer than three bits, add zeros on the left (leading zeros). They do not change the value. 3 Change each group into one octal digit.

Worked example

Convert 11010110₂ to octal

The number has 8 bits. 8 is not a multiple of 3, so add one leading zero to make 9 bits: 011010110. Group 011010110 Octal digit 326 Answer: 11010110₂ = 326₈ Check: 3 \times 64 + 2 \times 8 + 6 = 192 + 16 + 6 = 214, and 11010110₂ = 214 ✓

Do the reverse: write each octal digit as three bits, then join them. You may drop leading zeros at the very start of the answer.

Number base converter

From

NumberTo

Binary (2)

11010110

Octal (8)

326

Decimal (10)

214

Hex (16)

Working: multiply each digit by its place value, then add

128 + 64 + 0 + 16 + 0 + 4 + 2 + 0 = 214

Answer: 11010110₂ = 214₁₀

Try it:

Set To to Octal to see the grouping and padding. Then set From to Octal and To to Binary.

Practice

How many leading zeros must you add to 1011011₂ before grouping it in threes?