The binary number "111111" represents a value in the base-2 numeral system, which uses only two digits: 0 and 1. Each digit in a binary number is called a "bit." In this case, "111111" consists of six bits, and its value can be calculated by summing the powers of 2 for each bit position that is set to 1. When converted to decimal, "111111" equals 63. This conversion is done by calculating 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0, which results in 32 + 16 + 8 + 4 + 2 + 1. Understanding binary is essential in computing, as it forms the foundation of how data is processed in computers.