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Binary to Octal Converter

developer · number system

Convert Binary to Octal with a fixed input and output format, step-by-step formulas under the result, and reference tables. Parsing matches the main hub (0b, 0x, leading 0 for octal; one optional . for fractional digits on numeric bases; single character for character mode).

Calculator

From: Binary

To: Octal

Formulas

Enter a value → place-value expansion + division chain.

About Binary

Binary (base 2) uses digits 0 and 1. This tool accepts an optional 0b prefix. You may use one radix point; digits after it use negative powers of two (½, ¼, …). It is the native representation for digital logic and bitwise operations.

About Octal

Octal (base 8) uses digits 0–7. A leading 0 denotes octal in this converter (e.g. 0777). One radix point is allowed; fractional places use 8⁻¹, 8⁻², …. Grouping binary digits in threes maps cleanly to octal, which is why Unix file permissions often use it.

How to convert binary to octal

Three steps: symbols → the right math move for this pair → worked examples you can copy on paper. Numeric bases (binary, octal, decimal, hex) also support one radix point and digits after it; character mode stays a single code unit.

Step 1 — Identify the symbols

Input (Binary): Each position is either 0 or 1.

Output (Octal): Each digit is 0–7 (eight possibilities per position).

Dev note
  • Many tools allow a 0b prefix (e.g. 0b1010).
  • A leading 0 is often used to mark octal (e.g. 012).

Step 2 — The Two-Step Method (via Decimal)

First express the left format as a decimal value (one optional . for a fractional part is allowed on numeric bases), then rewrite that value in the right format. The calculator automates both steps.

Part A — Into decimal

Number positions from the right, starting at 0. At each position, multiply that digit by 2 raised to the position index, then add every term. The total is your decimal number.

Digits after the dot: use negative powers of 2 (2−1, 2−2, …). Each place is still (digit × weight); add the fractional side to the whole side.

Part B — Out of decimal

Repeated division by 8: same idea as binary, but divide by 8 each time. Remainders are octal digits (0–7), read bottom-up.

Fractional decimal values: convert the whole part with repeated division, then multiply the fractional part by the target base over and over; each integer you get is the next digit after the radix point (same idea the calculator shows in Formulas).

Step 3 — Worked examples

Two practice values in Binary, converted to Octal using the same rules as Step 2. Example 3 uses a fractional part (digits after the radix point); the hub and pair calculators accept a single . on binary, octal, decimal, and hex inputs.

Example 1

"1010" (Binary) → Octal.

Toward decimal

Binary "1010"
= 1×2³ + 0×2² + 1×2¹ + 0×2⁰
= 8 + 2
= 10  (decimal)

From decimal to output

Whole part — repeated division:
10 ÷ 8 = 1  R 2
1 ÷ 8 = 0  R 1

Read remainders bottom → top → 12

→ tool: 012

Verify: "1010" → 012

Example 2

"1111" (Binary) → Octal.

Toward decimal

Binary "1111"
= 1×2³ + 1×2² + 1×2¹ + 1×2⁰
= 8 + 4 + 2 + 1
= 15  (decimal)

From decimal to output

Whole part — repeated division:
15 ÷ 8 = 1  R 7
1 ÷ 8 = 0  R 1

Read remainders bottom → top → 17

→ tool: 017

Verify: "1111" → 017

Example 3

"1010.101" (Binary) → Octal.

Toward decimal

Binary "1010.101"
Left of . : 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 10
Right of .: 1×2^-1 + 0×2^-2 + 1×2^-3 = 0.5 + 0.125
= 10.625  (decimal)

From decimal to output

Whole part — repeated division:
10 ÷ 8 = 1  R 2
1 ÷ 8 = 0  R 1

Read remainders bottom → top → 12

Fractional part — multiply by 8, integer of each product = next digit after .
  0.625×8 = 5  →  5
Digits after . (in order): .5

→ tool: 012.5

Verify: "1010.101" → 012.5

Summary

To convert Binary to Octal, the tool first parses your input strictly as binary, producing a decimal value. For binary, octal, decimal, and hex, you may include one radix point and fractional digits; character input remains a single code unit with no dot. That value is formatted as octal using the same rules as the main Number System Converter (prefixes 0b, 0, 0x where applicable; character output uses symbolic names for common controls and requires a whole-number code point). Long fractional expansions are truncated to a fixed digit cap; ordinary floating-point rounding may appear in extreme cases.

Relationship context

Binary, Octal, and the other numeric bases on this site all describe the same numeric value; only the radix changes (including optional fractional digits after one dot). Moving between them is equivalent to changing how the value is written, not to scaling or unit conversion. Binary, octal, and hex align with bit boundaries (powers of two), while decimal is optimized for human arithmetic.

Conversion tables

Binary (input)Octal (output)
00
0b101
0b1002
0b1103
0b10004
0b10105
0b11006
0b11107
0b1000010
0b1001011
0b1010012
0b1111017
0b10000020
Binary (input)Octal (output)
0b1011013
0b100000040
0b10000000100
0b100000000200
0b1000000000400
0b100000000001000
0b1000000000002000
0b10000000000004000
0b1000000000000010000
0b10000000000000020000
0b100000000000000040000
0b10000000000000000100000
0b11111111111111110177777

More number system pairs

Other fixed input/output converters use the same parsing rules as the hub. Open any pair for the same calculator layout and reference tables.

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