How to Convert Binary to Octal
Converting binary to octal is one of the simplest number base conversions because octal is base-8 and binary is base-2, and 8 is a perfect power of 2 (). This means every single octal digit maps directly to exactly 3 binary bits. No complex arithmetic is needed — just group and substitute.
Step-by-Step 3-Bit Grouping Method
Follow these steps to convert any binary number (bin) to octal (oct) by hand:
Step 1: Write down the binary number
Start with your binary number. For example, 1101011.
Step 2: Group digits into sets of three from the right
Split the binary number into groups of 3 bits, starting from the rightmost digit. Pad the leftmost group with leading zeros if needed: 001 | 101 | 011.
Step 3: Convert each 3-bit group to its octal digit
Use the mapping: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7. So 001=1, 101=5, 011=3.
Step 4: Combine the octal digits
Read the octal digits from left to right:
Why Each Octal Digit Equals 3 Binary Bits
The mathematical basis for the binary in octal conversion is straightforward: a single octal digit represents values from 0 to 7, which is exactly the range of 3 binary bits (). This means:
Each octal digit maps to exactly one 3-bit binary group. This perfect power-of-2 relationship makes the bin to oct conversion a simple mechanical substitution with no division or multiplication required.
Binary to Octal Conversion Table
This is the essential quick-reference table for binary to octal conversion. Each 3-bit binary group maps to exactly one octal digit:
| Binary (3 bits) | Octal | Calculation |
|---|---|---|
| 000 | 0 | |
| 001 | 1 | |
| 010 | 2 | |
| 011 | 3 | |
| 100 | 4 | |
| 101 | 5 | |
| 110 | 6 | |
| 111 | 7 |
This table covers all 256 values from decimal 0 to 255 with their binary and octal equivalents. For values beyond 255, apply the same 3-bit grouping method to convert any binary number to octal.
Binary to Octal Conversion Examples
Below are worked examples showing the bin to oct conversion process step by step, from simple values to multi-digit numbers.
Convert 1101011 to Octal
Binary input: 1101011
1. Group into threes from right: 001 | 101 | 011
2. Convert each group:
3. Result:
Decimal equivalent: 107
Convert 11111111 to Octal (255 in decimal)
Binary input: 11111111
1. Group into threes from right: 011 | 111 | 111
2. Convert each group:
3. Result:
Decimal equivalent: 255 — the maximum value of an unsigned 8-bit byte.
Convert 111101101 to Octal (Unix Permission Example)
Binary input: 111101101 (rwxr-xr-x)
1. Group into threes from right: 111 | 101 | 101
2. Convert each group:
- (owner: rwx)
- (group: r-x)
- (others: r-x)
3. Result:
This is the familiar chmod 755 Unix permission — a practical example of how binary to octal conversion is used in real computing.
Binary to Octal in Programming
Most programming languages provide built-in functions for converting between binary and octal. Here are examples in the three most popular languages.
Python
# Convert binary string to octal string
binary_value = "1101011"
octal_value = oct(int(binary_value, 2))
print(octal_value) # '0o153'
# Remove '0o' prefix
octal_clean = oct(int(binary_value, 2))[2:]
print(octal_clean) # '153'
# One-liner bin to oct conversion
print(oct(int("11111111", 2))[2:]) # '377'JavaScript
// Convert binary string to octal string
const binaryValue = "1101011";
const octalValue = parseInt(binaryValue, 2).toString(8);
console.log(octalValue); // '153'
// For large binary values, use BigInt
const bigBin = "111101101";
const bigOct = BigInt("0b" + bigBin).toString(8);
console.log(bigOct); // '755'C
#include <stdio.h>
#include <stdlib.h>
int main() {
// Convert binary string to decimal, then print as octal
char *binary = "1101011";
long decimal = strtol(binary, NULL, 2);
printf("%lo\n", decimal); // prints: 153
// Using octal literals directly in C
int perms = 0755; // octal literal
printf("%o\n", perms); // prints: 755
return 0;
}Key Features
- Instant binary to octal conversion with real-time validation
- 3-bit grouping visualization showing the complete bin to oct conversion process
- Smart input validation for binary numbers (accepts only 0s and 1s)
- Automatic zero-padding for incomplete leftmost groups
- Support for converting any length of binary numbers to octal
- Simultaneous display of octal and decimal equivalents
- Step-by-step binary to octal conversion breakdown
- One-click copy for quick transfer of octal results
Applications of Binary to Octal Conversion
- Unix/Linux file permissions —
chmoduses octal to represent read (4), write (2), and execute (1) permission bits - Compact binary representation — octal provides a shorter way to express long binary numbers
- Digital circuit design and analysis requiring binary to octal conversions
- Assembly language programming and machine code analysis on legacy systems
- Computer science education for understanding number system relationships
- PDP and mainframe programming where octal notation is traditional
Related Converters
Explore our other number system and encoding converters for related tasks:
- Hex to Binary Converter — Convert hexadecimal numbers to binary with 4-bit group visualization
- Binary to Decimal Converter — Convert binary numbers to decimal (base-10) representation
- Binary Translator — Translate between binary and text in both directions
- Hex to Decimal Converter — Convert hexadecimal numbers to decimal values
- Base64 Encoder/Decoder — Encode and decode data in Base64 format
- ASCII Converter — Convert between ASCII characters and their numeric codes