Convert Binary to Octal

Binary-to-octal conversion is straightforward because each octal digit represents exactly 3 binary bits (since 2³ = 8). This makes the conversion a simple grouping exercise with no arithmetic required.

Step-by-step example — converting 110101110 to octal:

1. Group into 3-bit clusters from right to left: 110 | 101 | 110
2. Convert each group: 110=6, 101=5, 110=6
3. Combine: 656₈

So 110101110₂ = 656₈.

If the number of bits is not a multiple of 3, pad with leading zeros:

• 10110₂ becomes 010 110, which converts to 26₈

The complete 3-bit to octal lookup table:

Binary	Octal
000	0
001	1
010	2
011	3
100	4
101	5
110	6
111	7

Connection to file permissions:

This conversion is directly relevant to understanding Unix file permissions. The permission bits rwxr-xr-x translate to binary 111 101 101, which groups into octal as 7 5 5, giving the familiar chmod 755.

Binary-to-octal vs. binary-to-hex:

The choice between octal and hex depends on whether your data naturally groups into 3-bit or 4-bit units. File permissions use 3-bit groups (rwx), so octal is the natural fit. Byte-oriented data uses 4-bit nibbles, so hex is preferred. Understanding both conversions and when to apply each one is a key skill in systems programming, digital design, and computer architecture.