Convert between binary and decimal number systems with precise calculations, showing the conversion process and supporting both whole numbers and fractions.
Computers use binary (base-2) system, where only 0 and 1 are used, because electronic circuits can easily represent two states: on (1) and off (0).
Each binary digit (bit) represents a power of 2. A byte is 8 bits, which can represent 256 (2^8) different values, from 0 to 255.
Binary number system was popularized by Gottfried Wilhelm Leibniz in the 17th century, though the concept existed in ancient cultures like China.
Beyond computing, binary is used in telecommunications, digital signal processing, and encoding information in various fields like cryptography and data compression.