Synchronous 3-bit up/down counter

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SUMMARY

The discussion focuses on designing a synchronous 3-bit up/down counter that follows a specific decimal sequence: 0, 1, 3, 5, 7, 6, 4, 2, 0. The counter should increment when the UP/DOWN control input Y is set to 1 and decrement when Y is 0. The user encountered issues with the flip-flop transition table and the logic expressions, resulting in incorrect counting behavior in Logisim, where the output sequence was 0, 4, 5, 7, 6, 2, 3, 0 instead of the expected sequence.

PREREQUISITES
  • Understanding of synchronous counters
  • Familiarity with flip-flop transition tables
  • Experience with Logisim simulation software
  • Knowledge of binary number representation
NEXT STEPS
  • Review synchronous counter design principles
  • Study flip-flop transition table creation
  • Learn about state diagrams for digital circuits
  • Explore troubleshooting techniques in Logisim
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Electronics students, digital circuit designers, and anyone involved in implementing synchronous counters in digital systems.

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Homework Statement



Design and implement a synchronous 3-bit up/down counter with the following decimal code sequence: 0,1,3,5,7,6,4,2,0,… The counter should count “up” when an UP/DOWN control input Y is 1, and count “down” when the control input is 0.

  • Counting “up”
    decimal: 0,1,3,5,7,6,4,2,0,…
    binary: 000,001,011,101,111,110,100,010,000,…
  • Counting “down”
    decimal: 0,2,4,6,7,5,3,1,0,…
    binary: 000,010,100,110,111,101,011,001,000,…

2. The attempt at a solution

I don't know if the state diagram and Table are right but I am having trouble with the flip-flop transition table and the simplified logic expressions for flip-flop inputs. could someone help me out please

imageshack.us/f/822/statediagram2.png/

Picture of state diagrams and state table
 
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imageshack.us/f/822/statediagram2.png/

Picture of state diagrams and state table
 
Please can anyone help me i have built the circuit in logisim but its not counting to what it was suppose to

its counting 0,4,5,7,6,2,3,0

instead of 0,1,3,5,7,6,4,2,0
 

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