Galois Field GF(4)

Question:
Why is the table of GF(4) look like the one below? I know it has to do with the fact that 4 is composite
Let GF(4) = {0,1,B,D}

Addition:
$$
\begin{array}{c|cccc}
+ & 0& 1& B & D \\

\hline
0& 0 & 1 & B & D \\
1 & 1 & 0 & D & B \\
B & B & D & 0 & 1 \\
D & D & B & 1 & 0 \end{array}
$$

Multiplication:
$$\begin{array}{c|cccc}
\cdot & 0 & 1 & B & D \\
\hline

0 & 0 & 0 & 0 & 0 \\
1 & 0 & 1 & B & D \\
B & 0 & B & D & 1 \\
D & 0 & D & 1 & B
\end{array}$$