Binary Converter — Encode & Decode Binary
Binary Number Reference
Binary is a base-2 number system that uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from 2⁰ (1) on the right and increasing leftward. This makes binary the fundamental language of computers and digital systems.
To convert from binary to decimal, multiply each digit by its corresponding power of 2 and sum the results. For example, binary 1101 equals (1×8) + (1×4) + (0×2) + (1×1) = 13 in decimal.
| Decimal | Binary | Decimal | Binary |
|---|---|---|---|
| 0 | 0000 | 8 | 1000 |
| 1 | 0001 | 9 | 1001 |
| 2 | 0010 | 10 | 1010 |
| 3 | 0011 | 11 | 1011 |
| 4 | 0100 | 12 | 1100 |
| 5 | 0101 | 13 | 1101 |
| 6 | 0110 | 14 | 1110 |
| 7 | 0111 | 15 | 1111 |
When converting text to binary, this calculator uses 8-bit ASCII encoding, where each character is represented by an 8-digit binary number (byte). For example, the letter 'A' has ASCII value 65, which converts to binary 01000001.
Frequently Asked Questions
What is binary and why do computers use it?
Binary is a number system that uses only two digits: 0 and 1. Computers use binary because their electronic circuits can easily represent these two states as 'on' (1) and 'off' (0), making it the most efficient way for digital devices to process and store information.
How is text represented in binary using ASCII and UTF-8?
Text is converted to binary by assigning each character a numeric code, then converting that number to binary. ASCII uses 7-8 bits per character for basic English text, while UTF-8 uses 1-4 bytes per character to support all world languages and symbols.
What's the difference between binary and hexadecimal?
Binary uses base 2 (digits 0-1) while hexadecimal uses base 16 (digits 0-9 and letters A-F). Hexadecimal is often used as a shorthand for binary since each hex digit represents exactly 4 binary digits, making long binary numbers easier to read and write.
How do I manually convert decimal to binary using the division method?
Divide the decimal number by 2 repeatedly, keeping track of the remainders. The binary result is the remainders read from bottom to top. For example, 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1, giving us 1101 in binary.