Online Binary & Decimal Converter
Our free online Binary Decimal Converter allows you to convert between binary, decimal, and hexadecimal number systems. Perfect for students learning computer science and developers working with low-level data.
Features:
- Decimal to Binary: Convert base-10 numbers to binary representation.
- Binary to Decimal: Convert binary numbers back to decimal.
- Hex Conversion: Also supports decimal to hex and hex to decimal.
- Large Numbers: Handles numbers up to JavaScript's safe integer limit.
- Instant Results: Real-time conversion with no server requests.
1. Understanding Number Systems
Binary (Base 2): Uses only 0 and 1. Each position represents a power of 2.
Decimal (Base 10): Our everyday number system using 0-9.
Hexadecimal (Base 16): Uses 0-9 and A-F. Common in programming.
2. Binary Number System
Binary is the language of computers. Each binary digit (bit) can be 0 or 1. 8 bits make a byte, which can represent values from 0 to 255. Position values (right to left): 1, 2, 4, 8, 16, 32, 64, 128...
3. Converting Decimal to Binary
Method: Repeatedly divide by 2 and record remainders
Example: 13 → 13÷2=6 R1, 6÷2=3 R0, 3÷2=1 R1, 1÷2=0 R1
Read remainders bottom-up: 1101
Verify: 8+4+0+1 = 13 ✓
4. Converting Binary to Decimal
Method: Multiply each digit by its position value and sum
Example: 1101 → (1×8) + (1×4) + (0×2) + (1×1) = 13
Position values: 8, 4, 2, 1 (powers of 2)
5. Common Binary Values
1 byte (8 bits) max: 11111111 = 255
2 bytes (16 bits) max: 65,535
4 bytes (32 bits) max: 4,294,967,295
Powers of 2: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024...
This number system converter helps students and developers work with binary and decimal numbers.
100% client-side processing with instant results.
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