Binary to Octal and Octal to Binary Conversion — Step by Step Guide

Why Binary-Octal Conversion is Easy

Unlike decimal conversions that require division, binary-to-octal conversion uses a simple trick: group binary digits in sets of 3 from right to left. Each group directly maps to one octal digit. This works because 2³ = 8 — octal is a power-of-2 base.

🔧 Convert instantly: Binary to Octal Converter and Octal to Binary Converter — with step-by-step working shown.

Complete 3-Bit Reference Table

Binary (3-bit)	Octal Digit
000	0
001	1
010	2
011	3
100	4
101	5
110	6
111	7

Memorize this table — it’s all you need for any binary↔octal conversion.

Binary → Octal Conversion

Method:

1. Starting from the right, group binary digits into sets of 3
2. Pad the leftmost group with leading zeros if needed
3. Convert each 3-bit group to its octal equivalent

Example 1: Convert 110111010 to octal

Step 1: Group from right in 3s
110 | 111 | 010

Step 2: Convert each group
110 = 6
111 = 7
010 = 2

Answer: 672 (octal)

Example 2: Convert 11011 to octal

Step 1: Group (pad leftmost with zero)
011 | 011

Step 2: Convert
011 = 3
011 = 3

Answer: 33 (octal)

Example 3: Convert 1111111 to octal

Step 1: Group
001 | 111 | 111

Step 2: Convert
001 = 1
111 = 7
111 = 7

Answer: 177 (octal)

Octal → Binary Conversion

Method:

1. Take each octal digit separately
2. Convert to its 3-bit binary equivalent
3. Concatenate all groups

Example 1: Convert 537 to binary

5 = 101
3 = 011
7 = 111

Answer: 101011111 (binary)

Example 2: Convert 204 to binary

2 = 010
0 = 000
4 = 100

Answer: 010000100 → 10000100 (drop leading zero)

Example 3: Convert 7654 to binary

7 = 111
6 = 110
5 = 101
4 = 100

Answer: 111110101100 (binary)

Worked Examples Summary

Binary	Octal	Method
1010	12	001|010 → 1|2
110111	67	110|111 → 6|7
1111000	170	001|111|000 → 1|7|0
10110100	264	010|110|100 → 2|6|4
111111111	777	111|111|111 → 7|7|7

Binary-Octal vs Binary-Hex Grouping

Conversion	Group Size	Why
Binary ↔ Octal	3 bits	2³ = 8
Binary ↔ Hex	4 bits	2⁴ = 16

Both methods work on the same principle — the target base is a power of 2, so fixed-size bit groups map directly to single digits.

Common Mistakes

1. Grouping from left instead of right — always start from the rightmost bit
2. Forgetting to pad — if the leftmost group has fewer than 3 bits, add leading zeros
3. Confusing octal 8 and 9 — octal only uses digits 0-7, there is no 8 or 9
4. Dropping leading zeros in groups — keep all 3 bits per group during conversion

Real-World Applications

• Unix/Linux permissions: chmod 755 means rwx-r-x-r-x in binary: 111-101-101
• Legacy computing: Early PDP-8 computers used octal for instruction encoding
• Exam questions: BCA/BTech papers frequently ask binary↔octal conversions

Related Tools

• Number System Converter
• Binary to Octal Converter
• Octal to Binary Converter

Related Articles

• Octal Conversion Guide
• Binary to Hexadecimal Guide
• Binary Number System Explained

FAQ

Q: Why do we group in 3 bits for octal? A: Because 2³ = 8. Three binary bits can represent values 0-7, which exactly matches the octal digit range.

Q: What if my binary number isn’t divisible by 3? A: Pad with leading zeros on the left. Example: 1011 → 001 011 → 13 (octal).

Q: Is octal still used in modern computing? A: Less common than hex, but still used in Unix file permissions (chmod), some assembly languages, and occasionally in networking.

Q: Can I convert octal to hex directly? A: Easiest method: octal → binary (expand each digit to 3 bits) → hex (group in 4 bits). No need for decimal as intermediate.

Q: What’s the largest 3-digit octal number in binary? A: 777 (octal) = 111 111 111 = 511 (decimal). Nine binary bits maximum.