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Number bases, also known as numeral systems, are systems for representing numbers using symbols or digits. Each numeral system has a base, which is the number of unique symbols or digits it uses to represent values. Here’s an overview of some common numeral systems:
1. Decimal (Base 10):
• Base 10 uses ten unique digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
• This is the numeral system we use in everyday life for counting and arithmetic operations.
2. Binary (Base 2):
• Base 2 uses two unique digits: 0 and 1.
• Binary is commonly used in computer science and digital electronics because it corresponds directly to the on/off states of electronic switches.
3. Octal (Base 8):
• Base 8 uses eight unique digits: 0, 1, 2, 3, 4, 5, 6, and 7.
• Octal is used in some computer programming contexts and for representing sets of three binary digits.
4. Hexadecimal (Base 16):
• Base 16 uses sixteen unique digits: 0-9 and A-F (representing 10-15).
• Hexadecimal is commonly used in computing, especially for representing memory addresses, colors, and encoding binary data.
These are just a few examples of numeral systems, but there are theoretically an infinite number of possible bases. In each system, the value of a digit is determined by its position within the number and its place value, which is typically a power of the base. Understanding different numeral systems is important in mathematics, computer science, and other fields where numbers are manipulated and represented in various contexts.
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