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:

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