Octal to Binary Converter

Convert octal (base-8) numbers to binary instantly. Free online octal to binary calculator with conversion chart, examples, and step-by-step guide.

💡 Enter octal → get binary. Example: "72" → "111010".

From

Octal Input

Binary Output

How to Convert Octal to Binary

Step-by-step guide with examples

Input

Convert

Result

What is Octal to Binary Conversion?

Octal to binary conversion transforms base-8 numbers (digits 0-7) into base-2 numbers. Each octal digit maps directly to exactly 3 binary digits because 8=2³. This makes the conversion a simple lookup process.

How to Convert Octal to Binary Step-by-Step

1. Take each octal digit individually. 2. Convert each digit to its 3-bit binary equivalent. 3. Concatenate all 3-bit groups. Example: Convert 72 to binary: 7 = 111, 2 = 010 Result: 111010 Example: Convert 755 to binary: 7 = 111, 5 = 101, 5 = 101 Result: 111101101

Octal to Binary Chart

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

Common Use Cases

• Converting Unix file permissions to binary (755 → 111101101). • Digital system design with octal-based architectures. • Understanding legacy computing systems. • Analyzing PDP-11 and other octal-based machine code.

Frequently Asked Questions

6 common questions answered

6 Questions6 AnswersClick to expand

Q1How to convert octal to binary?

Replace each octal digit with its 3-bit binary equivalent: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111. Concatenate the groups.

Q2What is 47 octal to binary?

47 in octal = 100111 in binary. 4=100, 7=111 → 100111.

Q3What is 77 octal to binary?

77 in octal = 111111 in binary. 7=111, 7=111 → 111111 = 63 in decimal.

Q4What is 100 octal to binary?

100 in octal = 1000000 in binary. 1=001, 0=000, 0=000 → 001000000 = 64 in decimal.

Q5What is 377 octal to binary?

377 in octal = 11111111 in binary. 3=011, 7=111, 7=111 → 011111111. This equals 255 in decimal (max 8-bit value).

Q6How to convert octal to binary number?

Each octal digit (0-7) directly maps to 3 binary digits. Simply look up each digit in the conversion chart and write the 3-bit value. No complex math needed.