digital part1

A number system is a method of representing numbers using a set of digits and a base (radix). The most commonly used systems in digital electronics are: Binary (base-2), which uses digits 0 and 1 and is the fundamental language of digital hardware; Decimal (base-10), used in everyday calculations; Octal (base-8), which compresses binary using 3-bit groups; and Hexadecimal (base-16), which uses digits 0–9 and A–F and represents binary in 4-bit groups, making it compact and useful for memory addressing and debugging. In any positional number system, the value of a number is computed as the sum of each digit multiplied by its base power. Gray code is a special non-weighted binary code in which only one bit changes between consecutive numbers, minimizing switching errors and glitches. It is widely used in encoders, ADCs, and asynchronous FIFO designs, especially in clock domain crossing.