# Logic Design Questions and Answers – Equivalent and One-Hot State Assignments

This set of Logic Design Multiple Choice Questions & Answers (MCQs) focuses on “Equivalent and One-Hot State Assignments”.

1. What is the importance of equivalent states?
a) To simplify the circuitry
b) To change the flow of operation
c) To change the result of the operation
d) To reduce propagation delay

Explanation: State tables are used to describe different states of any finite state machine. If the present state, next state and output of any two states are same then they are called as equivalent states. Any number of equivalent states are simplified to one state to simplify the circuitry.

2. When two states of a state table are termed as equivalent states?
a) Only if the outputs are same
b) Only if the present states are same
c) If the next states are same
d) If the present state, next state and output are same

Explanation: State tables are used to describe different states of any finite state machine. If the present state, next state and output of any two states are same then they are called as equivalent states.

3. If there are 5 equivalent states found in any state table, then how many such states will be there in the reduced table?
a) 2
b) 3
c) 1
d) 0

Explanation: State tables are used to describe different states of any finite state machine. If the present state, next state and output of any two states are same then they are called as equivalent states. Any number of equivalent states are simplified to one state to simplify the circuitry. So there will only be one final state regardless of how many equivalent states are found.

4. What is the benefit of using a one-hot state assignment?
a) To reduce the number of states in a state table
b) To reduce number of operation
c) To reduce the number of cells required to realize each equation
d) To reduce number of flip-flops

Explanation: When designing with CPLDs and FPGAs, we should keep in mind that each logic cell contains one or more flip-flops. These flip-flops are there whether we use them or not. This means that it may not be important to minimize the number of flipflops used in the design. Instead, we should try to reduce the total number of logic cells. Using a one-hot state assignment may help to accomplish this.

5. Suppose there is a state machine with 4 states using a one hot key assignment, then how many flip-flops will be needed for this operation?
a) 2
b) 16
c) 4
d) Can’t be determined

Explanation: One-hot key assignment is needed to reduce the total number of cells in a state machine. The one-hot assignment uses one flip-flop for each state, so a state machine with N states requires N flip-flops. So, in this case, the operation will need 4 flip-flops.

6. Suppose there is a state machine with 4 states using a one hot key assignment, then which one of the following states will not be allowed in the operation?
a) 1000
b) 1100
c) 0100
d) 0010

Explanation: The one-hot assignment uses one flip-flop for each state, so a state machine with N states requires N flip-flops. Here 4 states are used, so there will be 24 = 16 states. But only one flip-flop is set to 1 in each state. Hence no two bits in a state can be 1 at same time. Hence 1100 cannot be obtained. The other 12 combinations are not used.

Sanfoundry Global Education & Learning Series – Logic Design.