Decimal Base Converter

Convert a decimal integer into binary, octal, and digit counts.

Inputs

Decimal Value

01,023

Calculation Results

Binary (Base 2 Representation)

1,11,11,111

Octal (Base 8 Representation)

377

Bits Required

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Formula & Mathematical Explanation

\displaystyle \text{Binary} = \text{dec}_2, \quad \text{Octal} = \text{dec}_8, \quad \text{Bits} = \lfloor\log_2(\text{dec})\rfloor + 1

Decimal numbers can be represented in other bases (such as base 2 for binary and base 8 for octal) by repeatedly dividing by the target base and reading the remainders in reverse. The minimum bits required is the binary logarithm rounded down plus one.