This depends on what kind of hexadecimal representation you're looking for; if you just want the numbers in base $16$ with the sign, drop the sign and convert them. If you want to convert the binary numbers to base $16$, use the following neat trick:
Since $16 = 2^4$, every four bits correspond to a single hexadecimal digit. So what you should do is pad the number with zeros (say you had $1110101110$, take $001110101110$), then group it into four digit groups ($0011~1010~1110$), then use the following table to translate:
$$ 0000 \to 0 $$
$$ 0001 \to 1 $$
$$ 0010 \to 2 $$
$$ 0011 \to 3 $$
$$ 0100 \to 4 $$
$$ 0101 \to 5 $$
$$ 0110 \to 6 $$
$$ 0111 \to 7 $$
$$ 1000 \to 8 $$
$$ 1001 \to 9 $$
$$ 1010 \to A $$
$$ 1011 \to B $$
$$ 1100 \to C $$
$$ 1101 \to D $$
$$ 1110 \to E $$
$$ 1111 \to F $$
For example, $0011~1010~1110 \to 3AE$
As for two's complement, the rule is $\tilde{} n = -n -1$, that is, for $8$ digit numbers $11111111$ represents $0-1 = -1$. Every number with a leading $1$ is negative, so the smallest is $10000000 = \tilde{} 01111111 = -127 - 1 = -128 $, and the largest is $01111111 = 127$.
If you are doing $R$'s complement, to get the negative of a number, change each digit $d$ to $R-1-d$, then add $1$ at the end, you do fine if $R$ is even. If $R$ is odd the divisions by $2$ don't come out even and you can't look at the leading digit to find the sign. For $R=4$, for example, the greatest three digit positive number is $133_4=31_{10}=\frac {4^3}2-1$ and the smallest negative number is $200_4=-32_{10}=-\frac {4^3}2$. For $R=3$ and three digit numbers, you would like the largest positive to be $111_3=13_{10}$ and the smallest negative to be $112_3=-13_{10}$, which fits your equation to within $1$, but you have to look at the whole number to know the sign.
Best Answer
There are (at least) three ways, but in both cases you have to know the bit width of the two complement. For this to be meaningful I would assume that we have 12 bits (otherwise the number would be positive)
The "computer" way is to bitwise invert the number and add $1$ and then negate it. In your example the bitwise inverse of $(F99)_{16}$ is $(066)_{16}$ (you can check by going via binary if you wish, but there's a trick to do this directly). Then convert that to decimal and you get $102$, add $1$ and you get $103$ so the result is the negation $-133$ of this.
The "mathematical" way is to convert it to decimal and then subtract $2^n$ where $n$ is the number of bits. $(F99)_{16}$ is $3993$ and $2^{12} = 4096$. Then subtracting you get $3993-4096=-103$.
The "direct conversion" way. Here we use how the two complement wraps at $(800\cdots)_{16}$. We convert to decimal in the normal way except we interpret the most significant hexit accordingly. Instead of having $8$ in this position denote $+8$ we let it denote $-8$ (and similarily $9$ denotes $-7$ and so on and finally $F$ denotes $-1$). This way we get $(-1)16^2 + 9 16^1 + 9 = -103$
(The trick to logically invert hexadecimal directly is to use that each hexit corresponds to four bits and you can either use a table for inversion of hexits or use the fact that inversion of a four bit number is the same as subtracting it from $15$).