Question

Let w be a binary string over {0, 1}* and d(w) denote its decimal value. The number of states in the minimal DFA corresponding to the set of all binary w, such that w ends with 1 end d(w) is even, is

• A. 1
• B. 4
• C. 3
• D. 6

Answer 1

The correct option is A 1

If a number is even. It will always end with a 0. So there is no such string w which is both even, as well as ends will a 1. Always remember, LSB = 0 implies number is even, else odd.
Hence language generated in this case will be empty.
Therefore for empty language, the number of states required = 1.