base
In mathematics, the term “base” refers to the number system used to represent numbers
In mathematics, the term “base” refers to the number system used to represent numbers. The base determines how the digits in a number are represented and how place value is assigned.
The most commonly used base is base 10, also known as the decimal system. In the decimal system, there are 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Place value is determined by powers of 10, with each digit representing a certain multiple of a power of 10. For example, in the number 987, the digit 9 represents 9 * 10^2 (900), the digit 8 represents 8 * 10^1 (80), and the digit 7 represents 7 * 10^0 (7). The total value of the number is the sum of these place values: 900 + 80 + 7 = 987.
Other commonly used bases include base 2 (binary), base 8 (octal), and base 16 (hexadecimal). In base 2, there are only two digits: 0 and 1. In base 8, there are eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. In base 16, there are 16 digits: 0-9, followed by A-F. These bases are frequently used in computer science and digital systems.
Changing the base of a number can alter its representation and place value. For example, the decimal number 13 can be represented as 1101 in binary (base 2) and 15 in octal (base 8).
Understanding different bases is important in several areas of mathematics, such as number theory, computer science, and cryptography. It allows for different ways of representing and manipulating numbers, and provides insights into the structure and patterns of numbers.
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