By using a Finite State Machine (FSM) to solve the following problem:
A sequence detector receives as its inputs the integers 1, 5, and 10 in an arbitrary order, one
integer at a time. Once the total sum of the received numbers exceeds the value 30, the FSM
outputs the integer value 1. Moreover, the difference between the total sum of the received
inputs and 30 must be covered using the smallest number of integer values 1 and 5. The FSM must
display the smallest number of the values that cover the difference between the total sum and
30.
To solve this problem using a Finite State Machine (FSM), we can design the FSM to keep track of the current sum of received inputs and transition between different states based on the input and the current sum. Here's how you can implement the FSM:
1. Start with an initial state, let's call it "START", where the current sum is zero.
2. Define three states: "SUM_1", "SUM_5", and "OUTPUT". These states represent different stages of the FSM.
3. Whenever an input of 1, 5, or 10 is received, transition to the corresponding state based on the current sum:
a. If the input is 1, transition to the "SUM_1" state and increment the current sum by 1.
b. If the input is 5, transition to the "SUM_5" state and increment the current sum by 5.
c. If the input is 10, transition directly to the "OUTPUT" state.
4. In the "OUTPUT" state, calculate the difference between the current sum and 30. If the difference is 0, output 1 and transition back to the "START" state. If the difference is greater than 0, output the difference and transition to the "START" state. If the difference is negative (which should never happen based on the problem statement), treat it as an error.
5. Repeat steps 3 and 4 until all inputs have been processed.
By following this FSM design, you can keep track of the total sum of received inputs and output the smallest number of values (1 or difference from 30) required to cover the difference between the total sum and 30.