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For example, 1234(base 5) when converted into base 10, is computed as : 1x5^3 + 2x5^2 + 3x5^1 + 4

Question is what is the logic behind doing this , Please Explain, Thanks in Advance.

user1718009
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Each digit is converted according to its place value. If a number is in base 10(that's decimal number) it is calculated in the same way. E.g if 1234 is in base 10 it can be calculated as 1*10^3+2*10^2+3*10^1+4*10^0 too. In short every number (in any base can be converted to decimal following the above pattern, even if the number is already in base 10).

Waqar Danish
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