Two's complement is a binary mathematical notation used to represent negative numbers in a way that the computer hardware can easily handle. Some synonyms for two's complement include complement arithmetic, radix complement, and base complement. Other related terms include unary negation, ones' complement, and sign-and-magnitude representation. While these terms may have slightly different meanings, they all relate to the representation of negative numbers in binary form. Understanding these concepts is essential for computer programming and digital communication systems, as they are used in a wide range of applications, from simple calculators to sophisticated computing systems.