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Number Theory: Addition

In this lab, you’ve learned about One Hot and Binary state machines and how to build them.

Rubric

Item Description Value
Summary Answers Your writings about what you learned in this lab. 25%
Question 1 Your answers to the question 25%
Question 2 Your answers to the question 25%
Question 3 Your answers to the question 25%

Name

Devon Humphrey, Matt Zhen

Summary

In this lab, we implemented One Hot and Binary encodings using D flip-flops and combinatorial logic. Finding the combinatorial logic for the Binary encodings was done using K-maps, while the One Hot logic was determined visually through drawing out the state table.

Lab Questions

Compare and contrast One Hot and Binary encodings

For starters, the one hot FSM needs a D flip-flop for each state being represented. Meanwhile the Binary encoding requires log base 2 (N states) D flip-flops to represent N states. For a large number of states, the number of D flip-flops needed may be inconvenient for one hot. Meanwhile for Binary encodings, some binary states might just not exist due to not being needed.

Which method did your team find easier, and why?

The D flip-flop was more straightforward in implementing, and thus it was easier. It was easier to determine visually what conditions would trigger what state based on the state table.

In what conditions would you have to use one over the other? Think about resource utilization on the FPGA.

The main condition we thought of is using binary encodings due to a large number of states. When there’s a large number of states, One Hot encodings are less efficient than Binary encodings due to needing more D flip-flops. Though for small numbers of states, since One Hot encodings really only have to look at the value of one D flip-flop, One Hot might be more ideal.

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