I have to compare $ (2)_{16} $ and $ (1.\overline{F})_{16} $.
$ (2)_{16} $ is very simple to compute, e.g. $ (2)_{16} = 2 \cdot 16^0 = 2 $. On the other hand, I dont know how to find out what $ (1.\overline{F})_{16} $ is because I don't understand what the letter $ F $ means.
Can anyone help me?
In number system of base $16$ we use letters $A,B,C,D,E,F$ for the digits $10,\,11\,\dots15$.
So, the other number is $$ 1 + \frac{15}{16}+\frac{15}{16^2}+\frac{15}{16^3}\dots$$ (Just as $1.\overset\bullet9\ =\ 1+\displaystyle\frac9{10}+\frac9{100}+\dots$ in decimal.)
This is the hexadecimal analgy to showing that $1.\bar{9} = 2$ in decimal.
The hexadecimal digits are $0-9, A, B, C, D, E, F$, where $A=10_{10}$, $B=11_{10}$, ... , $F=15_{10}$.
For the decimal case, you can express the repeating part as a geometric series, and you'd want to show that
$$\sum_{n=1}^{\infty} \frac{9 }{10^n} = 1.$$
For the hexadecimal case, replace the $9$ with a $15$, and the $10$ with a $16$.
In base 16, F corresponds to the number 15 (the highest one-digit number).
Hence you can see this as comparing $2$ and $1.999...$ in base 10. Can you resolve this now?
