Understanding number systems
The basics of the four most important number systems in computer science
The four most important number systems in mathematics and computer science are the binary system (base 2), the octal system (base 8), the decimal system (base 10) and the hexadecimal system (base 16). Each system uses a certain number of symbols (digits and letters) and arranges positions as powers of its base. Our number base converter instantly converts between all four systems.
In the decimal system (base 10), which we use in everyday life, each position represents a power of 10: the number 255 means 2 × 10² + 5 × 10¹ + 5 × 10⁰ = 200 + 50 + 5. In the binary system (base 2), 255 corresponds to the binary number 11111111, i.e. 8 set bits. In the hexadecimal system (base 16), 255 is represented as FF – particularly compact. In the octal system (base 8), the value is 377.
Converting between number systems follows a clear algorithm: first the input is converted to its decimal representation, then converted to the target system. In web design, hexadecimal color codes are important in practice (e.g. #1034A6 for Egyptian blue), while in systems programming, binary and hexadecimal representations of bitmasks and addresses are essential. Our converter saves manual conversion steps and prevents errors.
For students of computer science and mathematics, the number base converter is a valuable learning tool. You can try inputs in different bases and compare the results instantly. This strengthens the intuitive understanding of how number systems work and why certain representations are preferred in computer science. For example: a byte (8 bits) has the maximum value 11111111 in binary = FF in hexadecimal = 255 in decimal.