Convert base-8 to base-16 Online | Free numbers Converter

Number System

The base-8 number system, also known as the octal system, is a positional numeral system that uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each digit’s position represents a power of 8, starting from $8^0$ at the rightmost digit and increasing to the left. For example, the octal number 157 represents $1 \times 8^2 + 5 \times 8^1 + 7 \times 8^0 = 64 + 40 + 7 = 111$ in decimal. Octal is widely used in computing and digital electronics because it offers a compact way to represent binary numbers, with each octal digit corresponding to exactly three binary digits. This makes conversion between binary and octal simple and efficient. Octal numbers are often employed in programming, memory addressing, and digital circuit design, especially in older systems. Understanding base-8 also provides insight into positional numeral systems and arithmetic in non-decimal bases. Although hexadecimal (base-16) has largely replaced octal in modern computing, octal remains important for learning how computers represent and manipulate information. Studying base-8 helps build a strong foundation in number theory, digital logic, and alternative numeral systems, enhancing problem-solving skills and understanding of how different bases encode and process data.

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.