Decimal to Binary Converter - Base Converter

This decimal to binary converter is a professional online base conversion tool that supports bidirectional conversion between decimal and binary, with simple operation and accurate conversion. It is a practical tool for learning computer basics, programming development, network engineering, and other fields.

Features: Supports decimal to binary and binary to decimal bidirectional conversion; supports batch conversion to process multiple numbers at once; input validation ensures correct format; one-click copy of conversion results for easy use; completely free with no ads or limitations.

Highlights: Simple interface, easy operation, one-click base conversion; local processing with fast conversion speed; supports large number conversion with no length limit; responsive design supporting phones, tablets, computers and other devices.

Decimal is a counting system with base 10, using ten digits 0-9, which is the most commonly used number system in daily life. The characteristic of decimal is that every ten counts as one, and each digit's weight is a power of 10.

Binary is a counting system with base 2, using only two digits 0 and 1, which is the most basic number system in computers. In computers, all data is stored and processed in binary form because computer hardware can only recognize two states: on (1) and off (0).

Importance of base conversion: In computer programming, network engineering, digital circuit design, and other fields, base conversion is a fundamental skill. Understanding the conversion methods between decimal and binary helps in understanding how computers work.

1. Division by 2 method: Continuously divide the decimal number by 2 and record the remainder, then arrange the remainders from bottom to top. For example, decimal number 10 converts to binary: 10÷2=5 remainder 0, 5÷2=2 remainder 1, 2÷2=1 remainder 0, 1÷2=0 remainder 1, so the result is 1010.

2. Subtraction of powers method: Starting from the largest power of 2, subtract powers of 2 that are not larger than the current number, mark as 1, otherwise mark as 0. For example, decimal number 10, the largest power of 2 is 8 (2³), 10-8=2, mark as 1; 2 equals 2¹, mark as 1, other bits are 0, so the result is 1010.

3. Using calculator: Use a scientific calculator or online tools (like this tool) for conversion.

The calculation formula for decimal to binary conversion: Represent the decimal number as a sum of powers of 2, then set the corresponding bits to 1 and other bits to 0.

For example, decimal number 10 can be represented as 8 + 2 = 2³ + 2¹, so the corresponding binary number is 1010.

Decimal to binary mnemonic:

Divide by 2, get remainder, reverse order;

Stop when quotient is zero, combine remainders;

High bits on left, low bits on right.

Example: Decimal number 13, 13÷2=6 remainder 1, 6÷2=3 remainder 0, 3÷2=1 remainder 1, 1÷2=0 remainder 1, arrange remainders in reverse order to get 1101.

1. Select conversion direction: Decimal → Binary or Binary → Decimal.

2. Select input count: Single number or Multiple numbers (one per line).

3. Enter the number to convert: Decimal numbers contain only digits, binary numbers contain only 0 and 1.

4. Click the Convert button to view the conversion result.

5. Click the Copy button to copy the conversion result.

6. Click the Clear button to clear input and output content.