Convert base-13 to binary Online | Free numbers Converter

Number System

The base-13 number system, also called the tridecimal system, is a positional numeral system that uses thirteen symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and C, where A represents ten, B represents eleven, and C represents twelve in decimal. Each digit’s position represents a power of 13, starting from $13^0$ at the rightmost digit and increasing to the left. For example, the base-13 number 2B5 equals $2 \times 13^2 + 11 \times 13^1 + 5 \times 13^0 = 338 + 143 + 5 = 486$ in decimal. Base-13 is mainly used in theoretical mathematics and number theory to study alternative numeral systems, arithmetic patterns, and positional notation. Understanding base-13 allows learners to explore conversions between bases, analyze divisibility, and perform arithmetic in non-decimal systems. While it is not commonly used in everyday applications or computing, it provides a unique perspective on number representation and problem-solving. Studying the tridecimal system enhances comprehension of numeral systems beyond decimal, strengthens mathematical reasoning, and illustrates the flexibility of positional notation. It also serves as a foundation for exploring higher-level mathematics, coding theory, and abstract applications in theoretical number systems.

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Number System

The binary number system, also called base-2, is a positional numeral system that uses only two digits: 0 and 1. Each digit in a binary number represents a power of 2, starting with $2^0$ at the rightmost position and increasing to the left. For example, the binary number 1011 equals $1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 8 + 0 + 2 + 1 = 11$ in decimal. Binary is fundamental to digital electronics and computing because all digital devices, including computers and smartphones, operate using two states—commonly represented as on and off, high and low, or true and false. This simplicity allows circuits to reliably store, process, and transmit data. Binary numbers are used in various applications, including memory storage, processor instructions, networking protocols, and coding systems. Understanding binary is crucial for computer science, programming, and electronics, as it provides insight into how machines represent and manipulate information. Additionally, binary arithmetic and logic operations form the foundation for higher-level computations, making base-2 an essential concept in technology, digital communications, and modern computing systems.