\[ \text{Hexadecimal Representation Table:} \] \begin{array} {|r|r|}\hline Decimal & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline Hex & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & A & B & C & D & E & F \\ \hline \end{array}

\[ Hexadecimal → Decimal \] \[ \text{To convert from base } n \text{ to base to 10 use the following formula:} \] \[\sum_{i=0}^{k} a_i \cdot n^i\] \[i\text{ is the first base, where as } k \text{ is the last base. } a_i \text{ is the digit value as base } i. \] \[Example:\] \[\text{Let's convert the hex number } A2F \text{ to decimal.}\] \[\sum_{i=0}^{2} a_i \cdot 16^i =\] \[((A→10) *16^2)+(2*16^1)+((F→15)*16^0)=\] \[2,560 + 32 + 15=\] \[2607\]

\[ Decimal → Hexadecimal \] \[ \text{To convert from base } 10 \text{ to base to 16 use the following method:} \] \[Example:\] \[\text{1. Take the modulo of }n:2607 ≡ 16 =15\] \[\text{2. Take the floor of }\frac{n}{16}: \lfloor\frac{2607}{16}\rfloor = 162\] \[\text{3. 15 is the last digit of the hex value, and 162 will be used to find the next base.}\] \[\begin{aligned} 2607 ≡ 16 = 15\\ \lfloor \frac{2607}{16} \rfloor = 162\\ 162 ≡ 16 = 2\\ \lfloor \frac{162}{16} \rfloor = 10\\ 10 ≡ 16 = 10\\ \end{aligned}\] \[\text{10→A is the value of the first base, 2 is the second base & 15→F is the last base.}\] \[2607 = A2F\]