How to Set Up a State Table for a 2-bit Gray Code Counter?

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SUMMARY

The discussion focuses on setting up a state table for a 2-bit Gray code counter, specifically addressing the outputs y1 and y2 based on the control input x. When x = 0, the counter maintains its state, while x = 1 triggers a cycling through the Gray code sequence (00, 01, 11, 10) on clock pulses. The state table is confirmed to be correct, with y1 and y2 directly reflecting the current state of the counter, where y1 corresponds to the more significant bit and y2 to the less significant bit.

PREREQUISITES
  • Understanding of 2-bit Gray code sequences
  • Familiarity with flip-flop behavior in digital circuits
  • Knowledge of state tables in sequential logic design
  • Basic concepts of control inputs in digital counters
NEXT STEPS
  • Research the construction of state tables for different types of counters
  • Learn about the implementation of Gray code in digital systems
  • Explore flip-flop configurations and their applications in counters
  • Study the timing diagrams associated with Gray code counters
USEFUL FOR

Students studying digital electronics, engineers designing sequential circuits, and anyone interested in understanding Gray code implementations in counters.

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Homework Statement


A counter has two state outputs y1 (the more significant bit) and y2 (the less significant bit) and a control input x. When x = 0, the states of the counter’s flip-flops do not change. When x = 1, the states of the counter’s flip-flops cycle through the codes of a 2-bit Gray code sequence (00 – 01 – 11 – 10) on successive clock pulses.


Homework Equations





The Attempt at a Solution



I am having trouble setting up the state table. The gray code part is what's confusing me I think. Does anyone mind looking at my state table to verify if it's right. Also, how am I supposed to know what the outputs for y1 and y2 yield?

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Your state table is OK. y1 and y2 just output the current state of the counter, so y1=a and y2 = b
 

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