Binary to Octal Conversion Calculator
Binary and octal numbers are widely used in computer systems and electronics. While binary is the language of computers (0s and 1s), octal is used for grouping binary digits in a more human-readable form. Here, you can convert binary numbers directly to octal using this tool.
What are Binary Numbers?
Binary numbers are base-2 numbers that only use two digits: 0 and 1. Every binary digit (bit) represents a power of 2.
Examples:
1010101₂, 111100₂, 110011₁₀What are Octal Numbers?
Octal numbers are base-8 numbers. They use digits from 0 to 7. Each octal digit maps exactly to a group of three binary digits, which makes conversion between the two systems straightforward.
Examples:
7₈, 145₈, 76₈Binary to Octal Conversion Method
You can convert binary to octal in two main steps:
- Convert the binary number to decimal.
- Convert the resulting decimal number to octal.
Example: Convert 1010101₂ to octal:
Binary to Decimal:
= (1×2⁶) + (0×2⁵) + (1×2⁴) + (0×2³) + (1×2²) + (0×2¹) + (1×2⁰) = 64 + 0 + 16 + 0 + 4 + 0 + 1 = 85
Decimal to Octal: 85 ÷ 8 = 10 R5 → 10 ÷ 8 = 1 R2 → 1 ÷ 8 = 0 R1
Octal = 125₈
Binary to Decimal:
= (1×2⁶) + (0×2⁵) + (1×2⁴) + (0×2³) + (1×2²) + (0×2¹) + (1×2⁰) = 64 + 0 + 16 + 0 + 4 + 0 + 1 = 85
Decimal to Octal: 85 ÷ 8 = 10 R5 → 10 ÷ 8 = 1 R2 → 1 ÷ 8 = 0 R1
Octal = 125₈