Decimal to Binary, Hexadecimal & Octal Converter (with step‑by‑step expansion)

Any non-negative integer can be written in different bases. Below are the fundamental expansion formulas used by this calculator.

Binary (base 2) uses digits 0 and 1:

N = d_k−1 × 2^k−1 + … + d₁ × 2¹ + d₀ × 2⁰

Hexadecimal (base 16) uses digits 0–9 and A = 10, B = 11, C = 12, D = 13, E = 14, F = 15:

N = h_m−1 × 16^m−1 + … + h₁ × 16¹ + h₀ × 16⁰

Octal (base 8) uses digits 0–7:

N = o_n−1 × 8ⁿ⁻¹ + … + o₁ × 8¹ + o₀ × 8⁰

The converter below shows each representation together with its full expansion, exactly as you would write it on paper.

Number base converter

Insert any non‑negative integer → get binary, hex, octal + detailed expansions

Enter decimal number

Integer (≥ 0)

BINARY (base 2)

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HEXADECIMAL (base 16)

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A=10, B=11, C=12, D=13, E=14, F=15

OCTAL (base 8)

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After you press Convert, the calculator:

validates that you entered a non‑negative integer (no letters, no decimals).
converts the number using native .toString(base).
generates the polynomial expansion for each base: each digit is multiplied by the corresponding power of the base.
shows the full check that the sum equals the original decimal number.

The expansion uses red digits to highlight each coefficient. For hexadecimal, digits A‑F are shown in red as well.