Convert base-18 to base-2 Online | Free numbers Converter

Number System

The base-18 number system, also called the octodecimal system, is a positional numeral system that uses eighteen symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, and H, where A represents ten, B eleven, C twelve, D thirteen, E fourteen, F fifteen, G sixteen, and H seventeen in decimal. Each digit’s position represents a power of 18, starting from $18^0$ at the rightmost digit and increasing to the left. For example, the base-18 number 2G5 equals $2 \times 18^2 + 16 \times 18^1 + 5 \times 18^0 = 648 + 288 + 5 = 941$ in decimal. Base-18 is mainly used in theoretical mathematics, number theory, and educational exercises to explore alternative numeral systems, positional notation, and arithmetic patterns. Understanding base-18 allows learners to perform arithmetic operations, convert numbers between bases, and analyze properties of non-decimal systems. Although it is rarely applied in computing or daily life, studying the octodecimal system enhances problem-solving skills, logical reasoning, 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 how numbers can be efficiently represented and manipulated across diverse bases.

Number System

The base-2 number system, commonly called the binary system, is a positional numeral system that uses only two digits: 0 and 1. Each digit, known as a bit, represents a power of 2, with the rightmost position representing $2^0$, the next $2^1$, and so on. For example, the binary number 1101 equals $1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 8 + 4 + 0 + 1 = 13$ in decimal. Binary is fundamental to computing and digital electronics because electronic devices operate in two states: on and off, represented by 1 and 0. This simplicity allows computers to store, process, and transmit data reliably. Binary numbers are used in memory storage, processor instructions, networking, logic circuits, and coding systems. Understanding base-2 is crucial for computer science, programming, and engineering because it explains how machines represent and manipulate information. Binary arithmetic, logic operations, and data encoding form the foundation for higher-level computations, making the base-2 system indispensable for modern technology, digital communications, and computing systems.