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The use of different bases in mathematics serves several purposes like to solve different kinds of problems as in Calculus, Discrete Mathematics and in other forms of Mathematics too and mainly to make the use of calculations faster in Computer.
Question:
Solution:
Here are five basic purposes of using different bases in Mathematics:
1. Compact Representation: Different bases allow for more compact representation of numbers. For example, binary (base-2) is used in computing because it can represent numbers using only two symbols (0 and 1), which is efficient for electronic devices.
2. Ease of Computation: Some mathematical operations, such as division by factors of the base, are easier in certain bases. For example, division by 10 (in base-10) is easy because the result is simply a shift of the digits.
3. Representation of Fractions: Some bases, like octal (base-8) and hexadecimal (base-16), are convenient for representing fractions. This is important in computing, where fractions are commonly used in calculations.
4. Addressing Memory: In computing, memory addresses are often represented in hexadecimal because it is more compact than binary and easier to read than decimal.
5. Ease of Conversion: Converting between different bases can sometimes simplify calculations or make certain patterns more apparent. For example, converting between binary and hexadecimal is easier than converting between binary and decimal.
Overall, the use of different bases provides flexibility in representing and working with numbers, which is useful in various mathematical and computational contexts.
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