Decimal to Octal Conversion - Step-by-Step Guide with Examples

Decimal to Octal Conversion Guide

The decimal number system (base-10) is the most widely used numbering system in daily life. However, in computing and digital electronics, the octal number system (base-8) plays an important role. This guide explains how to convert decimal numbers to octal manually and using an online calculator.

What is the Octal Number System?

The octal number system uses eight digits: 0 to 7. Each digit's place value in octal is a power of 8. For example, the octal number 145₈ means:

\((1 \times 8^2) + (4 \times 8^1) + (5 \times 8^0) = 64 + 32 + 5 = 101_{10}\)

How to Convert Decimal to Octal?

Decimal to octal conversion involves dividing the decimal number by 8 repeatedly and recording the remainders. Here are the steps:

1. Divide the decimal number by 8.
2. Record the remainder.
3. Divide the quotient by 8 again.
4. Repeat until the quotient becomes 0.
5. Read the remainders in reverse order - that's your octal number.

Example: Convert 125₁₀ to Octal

Step 1: 125 \(\div\) 8 = 15 remainder 5
Step 2: 15 \(\div\) 8 = 1 remainder 7
Step 3: 1 \(\div\) 8 = 0 remainder 1
Result: Read from bottom to top \(\rightarrow\) 175₈

Decimal to Octal Conversion with Fraction

If the decimal number has a fractional part, you convert it separately:

1. Multiply the fractional part by 8.
2. Record the integer part of the result.
3. Repeat with the new fractional part.
4. Stop after reaching the desired precision (usually 4-6 digits).

Example: Convert 10.625₁₀ to Octal

Integer part: 10 \(\div\) 8 = 1 remainder 2 \(\rightarrow\) \(12_8\)
Fraction part: 0.625 \(\times\) 8 = 5.0 \(\rightarrow\) 5
Final Result: \(10.625_{10} = 12.5_8\)

Decimal to Octal Conversion Table

Use Our Decimal to Octal Calculator

Want a quick conversion? Use our free Decimal to Octal Calculator to get instant results with detailed steps!

Why Use Octal?

• Simplifies binary representation (every 3 binary digits = 1 octal digit).
• Used in early computer systems and file permissions (e.g., in Linux).
• Easier to read and shorter than binary.