Binary ↔ Decimal

Convert between binary (base-2) and decimal (base-10) number systems with step-by-step explanations.

Enter binary digits (0s and 1s) only. Supports fractional binary numbers.

How Binary-Decimal Conversion Works

Binary to Decimal

Each binary digit (bit) represents a power of 2. Starting from the rightmost bit (2⁰ = 1), each subsequent bit doubles in value (2¹ = 2, 2² = 4, 2³ = 8, etc.).

Example: 1011₂
1 × 2³ = 8
0 × 2² = 0
1 × 2¹ = 2
1 × 2⁰ = 1
Total: 11₁₀

Decimal to Binary

Divide the decimal number by 2 repeatedly, recording the remainders. The remainders (from bottom to top) form the binary representation.

Example: 11₁₀
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Binary: 1011₂

Pro Tips

  • Fractional binary: For numbers after the decimal point, use negative powers (2⁻¹ = 0.5, 2⁻² = 0.25, etc.)
  • Large numbers: Our tool supports binary numbers up to 64 bits long
  • Leading zeros: Binary numbers can have leading zeros without changing their value
  • Two's complement: For negative numbers in computing, binary uses two's complement representation