Convert base-16 to base-21 Online | Free numbers Converter

Number System

The base-16 number system, also known as the hexadecimal system, is a positional numeral system that uses sixteen symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F, where A represents ten, B eleven, C twelve, D thirteen, E fourteen, and F fifteen in decimal. Each digit’s position represents a power of 16, starting from $16^0$ at the rightmost digit and increasing to the left. For example, the hexadecimal number 2F3 equals $2 \times 16^2 + 15 \times 16^1 + 3 \times 16^0 = 512 + 240 + 3 = 755$ in decimal. Hexadecimal is widely used in computing and digital electronics because it provides a compact way to represent binary numbers, with each hex digit corresponding exactly to four binary digits. This simplifies conversions between binary and hexadecimal and makes it easier to read and write large binary values. Hexadecimal numbers are commonly used in programming, memory addressing, color codes in web design, and digital circuit design. Understanding base-16 is essential for computer scientists, engineers, and programmers, as it bridges the gap between human-readable numbers and machine-level binary code, enabling efficient computation, debugging, and data representation.

-21 Number System

The base-21 number system, also called the unvigesimal system, is a positional numeral system that uses twenty-one symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, and J, where A represents ten, B eleven, C twelve, D thirteen, E fourteen, F fifteen, G sixteen, H seventeen, I eighteen, and J nineteen, and K twenty in decimal. Each digit’s position represents a power of 21, starting from $21^0$ at the rightmost digit and increasing to the left. For example, the base-21 number 3K7 equals $3 \times 21^2 + 20 \times 21^1 + 7 \times 21^0 = 1323 + 420 + 7 = 1750$ in decimal. Base-21 is primarily used in theoretical mathematics, number theory, and educational exercises to explore alternative numeral systems, positional notation, and arithmetic patterns. Understanding base-21 allows learners to perform arithmetic operations, convert numbers between bases, and analyze properties of non-decimal systems. Although rarely applied in computing or daily life, studying the unvigesimal system enhances logical reasoning, problem-solving skills, and comprehension of abstract number representations. It also provides a foundation for exploring higher-level numeral systems, coding theory, and mathematical research, helping learners understand efficient ways to represent and manipulate numbers in diverse bases.