Convert base-11 to octal Online | Free numbers Converter

Number System

The base-11 number system, also called the undecimal system, is a positional numeral system that uses eleven distinct symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A, where A represents ten in decimal. Each digit’s position represents a power of 11, starting from $11^0$ at the rightmost digit and increasing to the left. For example, the base-11 number 2A3 equals $2 \times 11^2 + 10 \times 11^1 + 3 \times 11^0 = 242 + 110 + 3 = 355$ in decimal. Base-11 is mainly used in mathematical studies, number theory, and educational contexts to explore alternative numeral systems. It provides insights into arithmetic operations, positional notation, and conversion between bases. Understanding base-11 helps students and researchers recognize patterns in numbers, learn divisibility rules, and analyze properties of non-decimal systems. While it is not commonly used in computing or daily life, it serves as a useful tool for abstract mathematics and theoretical applications. Studying base-11 strengthens comprehension of how numbers can be represented in various bases, enhances problem-solving skills, and lays the groundwork for exploring higher-level numeral systems such as base-12, base-16, and beyond.

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Number System

The octal number system, also known as base-8, is a positional numeral system that uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each digit represents a power of 8, with the rightmost digit representing $8^0$, the next representing $8^1$, and so on. For example, the octal number 157 equals $1 \times 8^2 + 5 \times 8^1 + 7 \times 8^0 = 64 + 40 + 7 = 111$ in decimal. Octal was widely used in early computing systems because it provides a more compact representation of binary numbers: each octal digit corresponds exactly to three binary digits. This makes conversion between binary and octal straightforward and simplifies programming and memory addressing in older computer architectures. Although modern systems primarily use hexadecimal (base-16), octal remains important in some computing contexts, such as Unix file permissions, digital electronics, and certain embedded systems. Understanding octal helps in grasping how different number bases can efficiently represent information and interact with binary systems. It also provides a foundation for learning hexadecimal and other positional numeral systems used in digital technology.