Regular expression for binary representation of even numbers?

Question

I need help writing the regular expression over the alphabet (0,1) represent the even numbers in base ten. So basically the regular expression would show represent an even number in binary. (also if you know what the FSA would look for that it would help as well)

Answer 1

Here are the first few even natural numbers: $$ \begin{array}{r} 0 \\ 10 \\ 100 \\ 110 \\ 1000 \end{array} $$ Here are the first few odd natural numbers: $$ \begin{array}{r} 1 \\ 11 \\ 101 \\ 111 \\ 1001 \end{array} $$ Notice any pattern? You take it from here.