Question

Construct a Mealy machine that counts modulo 5,

Answer 1

Let's assume, E = {0, 1, 2, 3} (Input strings in Base 4 number system)

and,    = {0, 1, 2, 3, 4} (As we have to count modulo 5)

Transition Table:

States	0	1	2	3
-> q0	q0/0	q1/1	q2/2	q3/3
q1	q4/4	q0/0	q1/1	q2/2
q2	q3/3	q4/4	q0/0	q1/1
q3	q2/2	q3/3	q4/4	q0/0
q4	q1/1	q2/2	q3/3	q4/4

Required Mealy Machine:

Sample Input:

Let's take 12 as our input string (decimal equivalent of 12 is 6) and 6 mod 5 is 1.

Now, if we input 1 to q₀ it goes to q_1, and q₁ on getting input 2 goes to q₁ itself and gives the final output symbol 1 which is our required answer for 6 mod 5.