Binary to Octal Converter

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 (2³ = 8). 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

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.

• 001 = 1
• 101 = 5
• 011 = 3

Step 4: Combine the octal digits

Read the octal digits from left to right: 1101011₂ = 153₈

Why Each Octal Digit Equals 3 Binary Bits

A single octal digit represents values from 0 to 7, which is exactly the range of 3 binary bits (2³ = 8). Each octal digit d maps to exactly one 3-bit binary group. This perfect power-of-2 relationship makes the 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	0 × 4 + 0 × 2 + 0 × 1 = 0
001	1	0 × 4 + 0 × 2 + 1 × 1 = 1
010	2	0 × 4 + 1 × 2 + 0 × 1 = 2
011	3	0 × 4 + 1 × 2 + 1 × 1 = 3
100	4	1 × 4 + 0 × 2 + 0 × 1 = 4
101	5	1 × 4 + 0 × 2 + 1 × 1 = 5
110	6	1 × 4 + 1 × 2 + 0 × 1 = 6
111	7	1 × 4 + 1 × 2 + 1 × 1 = 7

This table covers all 8 possible 3-bit patterns. For values beyond 7, apply the grouping method to convert any binary number to octal.

Conversion Examples

Convert 1101011 to Octal

Binary input: 1101011

1. Group into threes from right: 001 | 101 | 011
2. Convert each group:
   • 001₂ = 1₈
   • 101₂ = 5₈
   • 011₂ = 3₈
3. Result: 1101011₂ = 153₈

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:
   • 011₂ = 3₈
   • 111₂ = 7₈
   • 111₂ = 7₈
3. Result: 11111111₂ = 377₈

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:
   • 111₂ = 7₈ (owner: rwx)
   • 101₂ = 5₈ (group: r-x)
   • 101₂ = 5₈ (others: r-x)
3. Result: 111101101₂ = 755₈

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.

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;
}

Applications of Binary to Octal Conversion

• Unix/Linux file permissions — chmod uses 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 — analysis requiring binary to octal conversions
• Assembly language programming — machine code analysis on legacy systems
• Computer science education — understanding number system relationships
• PDP and mainframe programming — where octal notation is traditional

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