Converting from Octal to Decimal.

Question

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?

Answer 1

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.