Question

chapter 7, problem 8c: (10 pts) design a synchronous counter that goes through the following sequence 6 5 4 1 2 3 and repeat using jk and d flip flops. show a state diagram, indicating what happens if it initially is in one of the unused states.

Answer 1

The question involves creating a synchronous counter with a specified state sequence using JK and D flip-flops. A state diagram will be used to represent the sequence 6, 5, 4, 1, 2, 3, and transitions will be made to ensure the counter loops back correctly even from unused states.

Step-by-step explanation:

The student's question is about designing a synchronous counter that follows a specific sequence using JK and D flip-flops. To meet the requirements of Chapter 7, Problem 8c, we need to establish a state diagram that describes the transitions between the states according to the provided sequence: 6, 5, 4, 1, 2, 3, and then repeats.

First, we would represent each state by a unique binary code, preferably minimized to use the least number of flip-flops. A state diagram can then be drawn where each circle represents one of the states (6, 5, 4, 1, 2, 3), and arrows represent transitions between these states. The counters should be designed in such a way that they naturally progress through this sequence. Additionally, for any unused state (those not in the sequence), the counter must transition back to the start of the sequence or an appropriate state within it. This ensures the counter always follows the sequence regardless of its initial state.

The state diagram will look similar to a circle with six nodes, and each node connected to the next corresponding state in the sequence. The transitions have to be carefully designed for the JK or D flip flops, so that the correct sequence is maintained. The design will also include logic to reset or direct the counter to the next correct state if it starts in an unused state.

Answer 2

A synchronous counter following a specific sequence can be designed by first representing the numbers in binary, creating a state diagram, and defining transition states. JK and D flip flop input equations are determined based on the sequence, and a logic circuit is built to implement these transitions. Unused states are handled with a reset condition to the initial state.

Step-by-step explanation:

Designing a Synchronous Counter with JK and D Flip Flops

To design a synchronous counter that follows the sequence 6, 5, 4, 1, 2, 3, we need to first consider the binary representations of these numbers and create a state table that defines the transitions. For a counter like this, we typically represent the sequence using a state diagram and then determine the necessary inputs for each flip flop to achieve the desired transitions.

The binary representations for the sequence are as follows:

The state diagram would include nodes for each of these states, with directed edges showing the path from one state to the next. For each unused state (000, 111, etc.), we would need to define a reset condition that brings the counter back to the initial state in the sequence (6, in this case).

A JK flip flop has two inputs, J and K, which control the flip flop's output. In designing the counter, input equations for the J and K inputs need to be created by comparing the current state to the next state and taking into account that in a JK flip flop:

We can use these rules to derive J and K inputs for each flip flop in our counter. A D flip flop simply takes the value at its D input and passes it to the output on the next clock edge. We need to determine the D inputs so that with each clock pulse, the flip flops transition to the correct next state in the sequence.

After establishing the J, K, and D inputs for each state transition, we would build a logic circuit that implements these expressions, using the appropriate number of JK and D flip flops. Finally, we would test the logic circuit to confirm that the counter moves through the correct sequence and properly handles unused states by resetting to the initial state when encountered.