Octal to Binary Converter

Convert Octal (Base 8) to Binary (Base 2) with step-by-step solution.

Valid digits: 01234567
255 (Base 8) = 10101101 (Base 2)
Step-by-Step Solution
1Convert Octal to Decimal:

Each digit × 8^position:

DigitValuePositionCalculationResult
2222 × 8^2128
5515 × 8^140
5505 × 8^05
Sum: 128 + 40 + 5 = 173
2Convert Decimal to Binary:

Divide by 2, collect remainders:

StepDividend÷ 2QuotientRemainderDigit
1173÷ 28611
286÷ 24300
343÷ 22111
421÷ 21011
510÷ 2500
65÷ 2211
72÷ 2100
81÷ 2011
Read bottom to top: 10101101
3Result:
255 (Base 8) = 10101101 (Base 2)

Conversion Table

DecimalOctalBinary
000
111
2210
3311
44100
55101
66110
77111
8101000
9111001
10121010
15171111
162010000
202410100
3240100000

255 (Base 8) in All Bases

Number SystemBaseValue
Binary210101101
Decimal10173
Hexadecimal16AD
Ternary320102
Quaternary42231
Quinary51143
Senary6445
Septenary7335
Duodecimal12125
Vigesimal208D
Duotrigesimal325D
Hexatrigesimal364T

Popular Conversions

How to Convert Octal to Binary

To convert from Octal (base 8) to Binary (base 2), first convert to decimal, then convert from decimal to Binary.

About Octal

Used in Unix file permissions. Uses digits: 01234567

About Binary

Used in computers and digital systems. Uses digits: 01