Question

Develop a circuit that cycles through your student number and displays the results on a 7-segmentdisplay (7SD). You can use a decoder chip (CD74HC4511E) to drive the 7SD. Sequential logic design: In this circuit, the sequential logic circuit uses flip-flops to go through your student number and will provide the inputs of the decoder chip.Dealing with repeated numbers: add additional flip-flops to count through which instance of a repeated number it is. Your student number is 4000190473.

Include:

Correct state transition diagram

Correct state transition table

Correct K-maps

Answer 1

Answer 2

To create a circuit that cycles through your student number (4000190473) and displays the results on a 7-segment display using a decoder chip (CD74HC4511E), we'll need to design a sequential logic circuit using flip-flops. We'll also handle repeated numbers by adding additional flip-flops to count through the instances of a repeated number.

Here's the step-by-step process to design the circuit:

Step 1: Determine the number of flip-flops required. To represent the student number 4000190473, we need a total of 10 flip-flops since there are 10 digits in the number.

Step 2: Create the state transition diagram. The state transition diagram represents the different states of the circuit and the transitions between them. Each state represents a particular digit of the student number.

Here's the state transition diagram for the given student number:

cssCopy code          ______
         |      |
         V      |
-> [q9] -- [q8] -- [q7] -- [q6] -- [q5] -- [q4] -- [q3] -- [q2] -- [q1] -- [q0]
   |    |      |
   '----'------'

The initial state is [q9], and it cycles through the flip-flops until it reaches [q0].

Step 3: Create the state transition table. The state transition table defines the next state of the circuit based on the current state and inputs.

Here's the state transition table for the given student number:

sqlCopy code+---------+---+---+---+---+---+---+---+---+---+---+---------+| Current | I | q9| q8| q7| q6| q5| q4| q3| q2| q1| Next    || State   | n |   |   |   |   |   |   |   |   |   | State   |+---------+---+---+---+---+---+---+---+---+---+---+---------+| 00000000| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100000000|| 100000000| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 010000000|| 010000000| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 001000000|| 001000000| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 000100000|| 000100000| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 000010000|| 000010000| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 000001000|| 000001000| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 000000100|| 000000100| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 000000010|| 000000010| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 000000001|| 000000001| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 000000000|+---------+---+---+---+---+---+---+---+---+---+---+---------+

Step 4: Simplify the state transition table and create K-maps. The Karnaugh maps (K-maps) help simplify the Boolean expressions for the inputs of the flip-flops.

Here are the K-maps for the flip-flops q9 to q0:

markdownCopy codeq9:  ________0| 0 | 0 |
1| 1 | 0 |

q8:  ________0| 0 | 0 |
1| 1 | 0 |

q7:  ________0| 0 | 0 |
1| 1 | 0 |

q6:  ________0| 0 | 0 |
1| 1 | 0 |

q5:  ________0| 0 | 0 |
1| 1 | 0 |

q4:  ________0| 0 | 0 |
1| 1 | 0 |

q3:  ________0| 0 | 0 |
1| 1 | 0 |

q2:  ________0| 0 | 0 |
1| 1 | 0 |

q1:  ________0| 0 | 0 |
1| 1 | 0 |

q0:  ________0| 0 | 0 |
1| 0 | 1 |

Step 5: Obtain simplified Boolean expressions. Using the K-maps, we can derive the simplified Boolean expressions for each flip-flop.

q9 = I q8 = q9 q7 = q8 q6 = q7 q5 = q6 q4 = q5 q3 = q4 q2 = q3 q1 = q2 q0 = q1'

Step 6: Implement the circuit. Using the simplified Boolean expressions, implement the circuit using D flip-flops.

Here's the circuit diagram:

rustCopy code              ____          ____          ____          ____          ____          ____          ____          ____          ____          ____          ____
I -----> D |    |  |        |    |  |        |    |  |        |    |  |        |    |  |        |    |  |        |    |  |        |    |  |        |    |  |        |    |  |        |    |  |        |    |  |        |    |
           | q9 |-->D-----> | q8 |-->D-----> | q7 |-->D-----> | q6 |-->D-----> | q5 |-->D-----> | q4 |-->D-----> | q3 |-->D-----> | q2 |-->D-----> | q1 |-->D-----> | q0 |-->D-----> | q0 |-->D-----> | q0 |
           |____|           |____|           |____|           |____|           |____|           |____|           |____|           |____|           |____|           |____|           |____|           |____|

Connect the outputs of each flip-flop (q9 to q0) to the corresponding