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I have the value $(3738)_8$ and I want to convert it to decimal. The answer i believe is $$(3 \times 8^3) + (7 \times 8^2)+ (3 \times 8^1) + (8 \times 8^0) = 2016$$. My question is that on some websites that have octal to decimal conversion calculators, inputting $3738$ does not generate a result because it isn't an octal number. Why is that?

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  • $\begingroup$ $3738$ is not allowed in octal. $\endgroup$ – Thomas Andrews Jan 24 '15 at 21:47
  • $\begingroup$ @Amzoti The question sheet says 3738 octal $\endgroup$ – Michel Tamer Jan 24 '15 at 21:57
  • $\begingroup$ @Amzoti Yes I did and I understand because if it is octal there is no point of having a digit of 8 octal because its equivalent of 10 octal. $\endgroup$ – Michel Tamer Jan 24 '15 at 22:02
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If you have a number in a base $b$, then the 'allowed' digits are normally $0,1,2,\ldots,b-1$. If you have a digit bigger or equal as $b$, then you could rewrite the number with out those digits. In your example the 'allowed' digits are $0,1,2,3,4,5,6,7$, so $8_8 = 10_8$, therefore $3738_8 = 3740_8$. But your calculation seems absolutely fine.

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