The total number of states and transitions required to form a moore machine that will produce residue mod 3

To design a Moore machine that will produce residue mod 3, we need to follow these steps:

1. Identify the States: The states of the machine are the possible remainders when a number is divided by 3. So, we have 3 states: 0, 1, and 2. These states represent the residue mod 3.

2. Identify the Transitions: The transitions are based on the input. If we consider binary input (0 and 1), then from each state, we have two transitions - one for input 0 and one for input 1.

   • If we are in state 0 (residue 0 mod 3), and the input is 0, we stay in state 0. If the input is 1, we move to state 1.
   • If we are in state 1 (residue 1 mod 3), and the input is 0, we move to state 2. If the input is 1, we move back to state 0.
   • If we are in state 2 (residue 2 mod 3), and the input is 0, we stay in state 2. If the input is 1, we move to state 1.

3. Identify the Output: In a Moore machine, the output is associated with the states. So, the output is the same as the state value (0, 1, or 2).

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