Decimal ↔ Binary Converter
Convert between decimal and binary number systems instantly
Enter base-10 number (0-1000000)
Base-2 binary representation
Conversion Result
42₁₀ = 101010₂
Decimal: 42 | Binary: 101010 | Hex: 2A
Binary Bit Visualization
Each bit represents a power of 2 (from right to left)
📚 Decimal to Binary Conversion Details
Decimal System (Base-10)
Uses digits 0-9. Each position represents a power of 10.
42 = 4×10¹ + 2×10⁰
Binary System (Base-2)
Uses digits 0 and 1. Each position represents a power of 2.
101010₂ = 1×2⁵ + 0×2⁴ + 1×2³ + 0×2² + 1×2¹ + 0×2⁰
Conversion Method
Repeated division by 2:
- Divide decimal number by 2
- Record remainder (0 or 1)
- Use quotient for next division
- Read remainders in reverse order
Common Uses
- Computer programming
- Digital electronics
- Data storage
- Network protocols
- Cryptography
📝 How to Convert Decimal to Binary
Step 1: Divide by 2
42 ÷ 2 = 21 (remainder 0)
42 ÷ 2 = 21 (remainder 0)
Step 2: Divide quotient by 2
21 ÷ 2 = 10 (remainder 1)
21 ÷ 2 = 10 (remainder 1)
Step 3: Continue dividing
10 ÷ 2 = 5 (remainder 0)
10 ÷ 2 = 5 (remainder 0)
Step 4: Continue dividing
5 ÷ 2 = 2 (remainder 1)
5 ÷ 2 = 2 (remainder 1)
Step 5: Continue dividing
2 ÷ 2 = 1 (remainder 0)
2 ÷ 2 = 1 (remainder 0)
Step 6: Last division
1 ÷ 2 = 0 (remainder 1)
1 ÷ 2 = 0 (remainder 1)
Step 7: Read remainders in reverse
Remainders: 0, 1, 0, 1, 0, 1
Reverse order: 101010
Remainders: 0, 1, 0, 1, 0, 1
Reverse order: 101010
📊 Conversion Table
| Decimal | Binary | Hex | Power of 2 |
|---|---|---|---|
| 0 | 0 | 0 | 2⁰ |
| 1 | 1 | 1 | 2⁰ |
| 2 | 10 | 2 | 2¹ |
| 4 | 100 | 4 | 2² |
| 8 | 1000 | 8 | 2³ |
| 16 | 10000 | 10 | 2⁴ |
| 32 | 100000 | 20 | 2⁵ |
| 64 | 1000000 | 40 | 2⁶ |
| 128 | 10000000 | 80 | 2⁷ |
| 255 | 11111111 | FF | 2⁸-1 |
❓ Frequently Asked Questions
Q: What is the decimal number system?
A: Decimal is base-10 system using digits 0-9. It's the standard system for everyday counting.
Q: What is the binary number system?
A: Binary is base-2 system using only 0 and 1. It's fundamental to digital computers and electronics.
Q: How do I convert decimal to binary manually?
A: Divide the decimal number by 2 repeatedly, recording remainders. The binary equivalent is the remainders read in reverse order.
Q: What is the maximum number I can convert?
A: This converter handles numbers up to 1,000,000 (1 million). For larger numbers, the binary result may be very long.