Decimal to Binary Converter
Free online tool to instantly convert decimal (Base 10) to binary (Base 2). Includes quick conversion tables and step-by-step mathematical explanations.
How to convert Decimal to Binary
Converting from Decimal (Base 10) toBinary (Base 2) involves positional value evaluation.
Convert Decimal to Binary
Divide the decimal value repeatedly by 2. Record the remainders after each division. The final binary representation is formed by reading the remainders in reverse order (bottom to top).
Decimal to Binary Quick Conversion Table
Common values converted between Decimal (Base 10) and Binary (Base 2):
| Decimal (10) | Binary (2) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 11 | 1011 |
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
| 16 | 10000 |
| 32 | 100000 |
| 64 | 1000000 |
| 100 | 1100100 |
| 255 | 11111111 |
Decimal to Binary Frequently Asked Questions
Common questions and step-by-step mathematical answers about converting Decimal (Base 10) to Binary (Base 2).
1How do you convert decimal to binary?↓
To convert decimal (base-10) to binary (base-2), use the repeated division-by-2 method. Divide your integer by 2, record the remainder, and divide the quotient by 2 again until the quotient is 0. Read the remainders from last to first (bottom to top).
2What is the formula for converting decimal to binary?↓
The mathematical relationship expresses the decimal value as the sum of powers of 2: N₁₀ = dₙ·2ⁿ + ... + d₁·2¹ + d₀·2⁰, where each dᵢ ∈ {0, 1}.
3How do you convert a decimal number to binary manually?↓
Example with 19: 19÷2 = 9 (rem 1), 9÷2 = 4 (rem 1), 4÷2 = 2 (rem 0), 2÷2 = 1 (rem 0), 1÷2 = 0 (rem 1). Reading bottom-to-top gives 10011₂.
4What is 10 in binary?↓
10₁₀ = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰) = 8 + 0 + 2 + 0 = 1010₂.
5What is 25 in binary?↓
25₁₀ = 16 + 8 + 1 = 2⁴ + 2³ + 2⁰ = 11001₂.
6What is 50 in binary?↓
50₁₀ = 32 + 16 + 2 = 2⁵ + 2⁴ + 2¹ = 110010₂.
7What is 100 in binary?↓
100₁₀ = 64 + 32 + 4 = 2⁶ + 2⁵ + 2² = 1100100₂.
8How do you convert decimal fractions to binary?↓
Multiply the fractional part by 2. If the product is ≥ 1, record 1 and keep the fractional part; otherwise record 0. Repeat until the fractional part is 0 or desired precision is achieved. Example: 0.625 × 2 = 1.25 (1), 0.25 × 2 = 0.5 (0), 0.5 × 2 = 1.0 (1) → 0.101₂.
9Can negative decimal numbers be converted to binary?↓
In standard computers, two's complement is used: invert all bits of the positive binary representation and add 1. In standard mathematical notation, a simple minus prefix is written (e.g., -10₁₀ = -1010₂).
10How does the decimal to binary conversion work?↓
Since each position in a binary number represents a power of 2 (1, 2, 4, 8, 16, 32, ...), the conversion breaks down the decimal integer into the unique combination of these powers.