Number of states require to accept string ends with 10.

To design a Finite Automaton (FA) that accepts all the strings ending with '10', we need 3 states. Here's the step by step process:

1. Define the states: Let's define three states q0, q1, and q2. Here, q0 is the start state and q2 is the final state.

2. Define the transitions: The transitions will be as follows:

   • From state q0, on input 1, the FA should move to state q1. This is because we are looking for strings that end with '10', and we have encountered '1' which could potentially be the start of '10'.
   • From state q0, on input 0, the FA should stay in state q0. This is because '0' does not contribute to a string ending in '10'.
   • From state q1, on input 1, the FA should stay in state q1. This is because encountering another '1' after a '1' could still potentially lead to a string ending in '10'.
   • From state q1, on input 0, the FA should move to state q2. This is because after encountering '1', we have now encountered '0', so we have a string ending in '10'.
   • From state q2, on input 0 or 1, the FA should stay in state q2. This is because once we have a string ending in '10', any further inputs do not change this.

3. Define the start and accept states: The start state is q0 and the accept state is q2. The FA will start in state q0 and will accept if it is in state q2 when all inputs have been read.

So, the number of states required to accept a string that ends with '10' is 3.

To design a Finite Automaton (FA) that accepts all the strings ending with '10', we need 3 states. Here's the step by step process:

1. Start with an initial state (q0). This state represents that we have not received any input yet.

2. If we get input '1', we move to a new state (q1). This state represents that we have seen a '1' and we are expecting a '0' to complete '10'.

3. If we get input '0' while we are in state q1, we move to a new state (q2). This state represents that we have seen '10' and the string ends with '10'.

4. If we get input '1' while we are in state q2, we stay in state q2 because the string still ends with '10'.

5. If we get input '0' while we are in state q2, we move back to state q1 because the string now ends with '00' and we are expecting a '1' to complete '10'.

6. If we get input '0' while we are in state q0 or q1, we stay in the same state because the string does not end with '10'.

7. If we get input '1' while we are in state q2, we stay in the same state because the string still ends with '10'.

So, the minimum number of states required to accept strings that end with '10' is 3.