Synchronous 3-bit up/down counter

AI Thread Summary
The discussion focuses on designing a synchronous 3-bit up/down counter that follows a specific decimal sequence. The counter should increment when the UP/DOWN control input is 1 and decrement when it is 0. The user is struggling with the state diagram, transition table, and logic expressions for the flip-flops, leading to incorrect counting in their Logisim implementation. Instead of the expected sequence of 0,1,3,5,7,6,4,2,0, the counter is incorrectly counting 0,4,5,7,6,2,3,0. Assistance is requested to resolve these issues and achieve the desired counting behavior.
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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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