How do you convert binary to octal?

Group the binary digits into sets of three, starting from the right. If the leftmost group has fewer than three digits, pad it with leading zeros. Then convert each 3-bit group to its octal equivalent (000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7). For example, binary 110101 groups as 110 101, which converts to octal 65.

What is the octal number system?

The octal number system (base 8) uses eight digits: 0 through 7. Each digit position represents a power of 8, similar to how decimal positions represent powers of 10. Octal was historically popular in computing because early computers used 12-bit, 24-bit, or 36-bit words, all of which divide evenly into 3-bit groups. It remains used in Unix/Linux file permissions and some programming contexts.

Why are binary digits grouped in threes for octal?

Binary digits are grouped in threes because 2^3 = 8, meaning three binary bits can represent exactly the same range of values as one octal digit (0-7). This mathematical relationship makes conversion between binary and octal a simple pattern-matching exercise. Each group of three bits maps directly to one octal digit without any complex arithmetic, making the conversion fast and error-free.

What is 111 in octal?

Binary 111 equals 7 in octal. The calculation is: (1 x 2^2) + (1 x 2^1) + (1 x 2^0) = 4 + 2 + 1 = 7. This is the largest single octal digit, since 111 is the largest 3-bit binary number. Any binary number with more than three digits would require multiple octal digits. For example, binary 1111 groups as 001 111, converting to octal 17.

Where is octal used in computing?

Octal is most commonly used in Unix/Linux file permissions, where permissions for owner, group, and others are each represented as a 3-bit value (read=4, write=2, execute=1). For example, chmod 755 sets rwxr-xr-x. Octal is also used in some programming languages as a number literal prefix (e.g., 0o755 in Python, 0755 in C), and historically in PDP minicomputers and early mainframes.

How do you convert octal back to binary?

Replace each octal digit with its 3-bit binary equivalent. The mapping is: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111. For example, octal 347 converts to binary by replacing 3 with 011, 4 with 100, and 7 with 111, giving 011100111. You can remove leading zeros to get 11100111. This direct substitution works because each octal digit perfectly represents three binary bits.

What is the difference between octal and hexadecimal?

Octal (base 8) groups binary digits in threes and uses digits 0-7, while hexadecimal (base 16) groups binary digits in fours and uses digits 0-9 plus A-F. Hexadecimal is more common in modern computing because most systems use 8-bit bytes, 16-bit, 32-bit, or 64-bit words, all of which divide evenly into 4-bit groups. Octal was more popular with older systems that used word sizes divisible by 3.

Can you convert binary to octal without grouping?

Yes, you can convert binary to octal by first converting binary to decimal and then dividing the decimal by 8 repeatedly, recording the remainders. However, the 3-bit grouping method is significantly faster and less error-prone. For example, converting 110101 via decimal: (1x32)+(1x16)+(0x8)+(1x4)+(0x2)+(1x1) = 53, then 53/8 = 6 remainder 5, giving octal 65. With grouping: 110 101 = 6 5 = 65. The grouping method avoids all arithmetic and is the preferred approach for bin to oct conversion.

Binary to Octal Converter — Free Online Bin to Oct Calculator

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 ( $2^3 = 8$ ). 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

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: $1101011_2 = 153_8$

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 ( $2^3 = 8$ ). This means:

(d)_{8} = (b_2 b_1 b_0)_2 \quad \text{where } d \in \{0,1,...,7\}

Each octal digit $d$ 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	$0 \times 4 + 0 \times 2 + 0 \times 1 = 0$
001	1	$0 \times 4 + 0 \times 2 + 1 \times 1 = 1$
010	2	$0 \times 4 + 1 \times 2 + 0 \times 1 = 2$
011	3	$0 \times 4 + 1 \times 2 + 1 \times 1 = 3$
100	4	$1 \times 4 + 0 \times 2 + 0 \times 1 = 4$
101	5	$1 \times 4 + 0 \times 2 + 1 \times 1 = 5$
110	6	$1 \times 4 + 1 \times 2 + 0 \times 1 = 6$
111	7	$1 \times 4 + 1 \times 2 + 1 \times 1 = 7$

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:

$001_2 = 1_8$
$101_2 = 5_8$
$011_2 = 3_8$

3. Result: $1101011_2 = 153_8$

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:

$011_2 = 3_8$
$111_2 = 7_8$
$111_2 = 7_8$

3. Result: $11111111_2 = 377_8$

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:

$111_2 = 7_8$ (owner: rwx)
$101_2 = 5_8$ (group: r-x)
$101_2 = 5_8$ (others: r-x)

3. Result: $111101101_2 = 755_8$

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 — 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 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

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Binary to Octal Converter