The total number of states and transitions required to form a moore machine that will produce residue mod 3.ans.2 and 42 and 53 and 63 and 5 Previous Marked for Review Next

To design a Moore machine that produces a residue modulo 3, we need to consider the possible remainders when a number is divided by 3. These are 0, 1, and 2. Therefore, we need 3 states to represent these remainders.

Step 1: Define the states Let's define the states as Q0, Q1, and Q2 where Q0 represents a remainder of 0, Q1 represents a remainder of 1, and Q2 represents a remainder of 2.

Step 2: Define the transitions Next, we need to define the transitions between these states. The transitions will be based on the input, which can be either 0 or 1.

• From state Q0, if the input is 0, we stay in Q0 because 0 modulo 3 is still 0. If the input is 1, we move to Q1 because 1 modulo 3 is 1.
• From state Q1, if the input is 0, we move to Q2 because (12) modulo 3 is 2. If the input is 1, we move back to Q0 because (12 + 1) modulo 3 is 0.
• From state Q2, if the input is 0, we move to Q1 because (22) modulo 3 is 1. If the input is 1, we stay in Q2 because (22 + 1) modulo 3 is 2.

Step 3: Define the output Finally, we need to define the output for each state. In a Moore machine, the output is determined by the current state. Since we are producing a residue modulo 3, the output for each state will be the remainder when the current state number is divided by 3. Therefore, the output for Q0 is 0, for Q1 is 1, and for Q2 is 2.

So, the total number of states required is 3 and the total number of transitions is 6 (2 transitions from each state).