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iceblits
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Has anyone come across how to find "the base-b expansion" of a number? I don't think its tricky or anything I just don't know what it's referring to...
iceblits said:Has anyone come across how to find "the base-b expansion" of a number? I don't think its tricky or anything I just don't know what it's referring to...
Base-b expansion of a number is a method of representing a number in a different base, or number system. It involves writing the number as a sum of multiples of powers of the new base, with the coefficients being the digits of the new number system.
The decimal system, or base-10 system, uses 10 digits (0-9) to represent all numbers. Base-b expansion uses a different number of digits depending on the base, and the value of each digit is determined by its position in the number.
Base-b expansion allows us to easily convert numbers between different number systems. It is also useful in computer programming, cryptography, and other fields that involve working with different number bases.
Yes, any number can be represented in base-b expansion. However, some numbers may have repeating or never-ending expansion in certain bases, such as 1/3 in base-10.
To convert a number from base-b expansion to decimal, you can use the formula:
decimal number = (first digit * b^(n-1)) + (second digit * b^(n-2)) + ... + (last digit * b^0)
where b is the base and n is the number of digits in the expansion. For example, to convert 1101 from base-2 to decimal, we have: (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0) = 8 + 4 + 0 + 1 = 13.