Convert between binary, decimal, and text. Encode text to binary or decode binary to readable text.
Binary is a base-2 number system that uses only two digits: 0 and 1. It's the foundation of digital computing and is used to represent all data in computers.
In binary, each position represents a power of 2, starting from the rightmost digit (2^0 = 1) and increasing as you move left (2^1 = 2, 2^2 = 4, 2^3 = 8, etc.).
To convert binary to decimal, multiply each digit by its corresponding power of 2 and sum the results.
Binary: 1 0 1 1
Position values: 2^3 2^2 2^1 2^0
Calculation: 1×8 + 0×4 + 1×2 + 1×1
Decimal: 8 + 0 + 2 + 1 = 11
To convert decimal to binary, divide the number by 2 repeatedly and record the remainders in reverse order.
Decimal: 13
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Binary (reading remainders from bottom to top): 1101
In computing, text is converted to binary using character encoding standards like ASCII or UTF-8. Each character is represented by a specific binary sequence.
Computers use binary because electronic components can easily represent two states: on/off, high/low voltage, or magnetic polarities. This makes binary the most natural number system for digital electronics.
A bit (binary digit) is the smallest unit of data in computing, representing either a 0 or a 1. A byte is a group of 8 bits, which can represent 256 different values (2^8).
Negative numbers are typically represented using methods like two's complement, where the leftmost bit indicates the sign (0 for positive, 1 for negative) and the remaining bits represent the magnitude with some mathematical adjustments.