The binary number system is a way of representing numbers using only two digits: 0 and 1. This system is fundamental in computing and digital electronics because it aligns with the two states of a transistor, which can be either off (0) or on (1). Each digit in a binary number is called a bit, and multiple bits can be combined to represent larger values. In binary, each position represents a power of 2, starting from the rightmost bit, which is 2^0. For example, the binary number 101 represents the decimal number 5 because it is calculated as 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0. This simple yet powerful system is the foundation of modern computing.