Binary to Octal

Computer Science Base Radix & 3-Bit Grouping

Because 8 = 2^3, converting between binary (base 2) and octal (base 8) requires no complex arithmetic—simply map each 3-bit binary triad directly to a single octal digit.

3-Bit Triad Conversion Table

• 000 = 0

• 001 = 1

• 010 = 2

• 011 = 3

• 100 = 4

• 101 = 5

• 110 = 6

• 111 = 7

Unix POSIX File Permission Octal Equivalents

• Read (r): 4 = 100_2

• Write (w): 2 = 010_2

• Execute (x): 1 = 001_2

• 755 Mode: rwxr-xr-x = 111 101 101_2

How to Use This Calculator

Enter your Number String to Convert (e.g. 110101111) and Conversion Direction — choose from Binary to Octal (Base 2 → Base 8), Octal to Binary (Base 8 → Base 2). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Formula Reference: Binary to Octal

Input variables:

inputValueString — Number String to Convert

conversionDirectionSelect — Conversion Direction

Computed outputs:

convertedRadixString — Converted Radix Result

octalRepresentation — Octal Value (Base 8)

binaryRepresentation — Binary Value (Base 2)

decimalRepresentation — Decimal Value (Base 10)

hexRepresentation — Hexadecimal (Base 16)

Mathematical relationships extracted from calculation logic:

triadArray = paddedBin.match(/.1,3/g) || []

posixStr = octToRwx(octStr[0]) + octToRwx(octStr[1]) + octToRwx(octStr[2])

Standard: NIST Handbook 44 and BIPM SI unit definitions

Worked Example

The binary sequence 110101111 partitions into 3-bit triads 110 (6), 101 (5), and 111 (7), translating directly to octal 657.

Understanding Your Result

Unit conversion precision: round to the same number of significant figures as your original measurement. Converting 6 feet to meters gives 1.8288 m — but if your measurement was approximate (±1 inch), expressing more than 2 decimal places is false precision. For international trade and technical specifications, SI units (meters, kilograms, liters) are the standard. US customary units (feet, pounds, gallons) differ from Imperial UK units: 1 US gallon = 3.785 L vs. 1 UK gallon = 4.546 L.