Final answer:
To design a decade counter with D flip-flops, one must establish a transition table, determine the next state equations, connect the flip-flop outputs to their D-inputs accordingly, and include a resetting logic that returns the counter to 0 after reaching 9.
Step-by-step explanation:
To design a decade counter using D flip-flops that counts in the given sequence, we need to design a circuit that counts from 0 to 9 and then resets back to 0. The sequence provided corresponds to the binary representation of the numbers 0 to 9. Since we are dealing with D flip-flops, we will establish the necessary transition table that indicates the present state and the next state.
Each D flip-flop holds one bit of the 4-bit binary number, with Q3 being the most significant bit (MSB) and Q0 being the least significant bit (LSB). We need to determine the inputs to D flip-flops (D3, D2, D1, D0) based on the current output states of the flip-flops (Q3, Q2, Q1, Q0).
The D input for each flip-flop is the next state of that flip-flop. When you express the next state of each flip-flop in terms of the current states, you will have a set of equations. You can then build the circuit by connecting the outputs of the flip-flops to the D inputs according to these equations.
To reset the counter from 1001 to 0000, we need additional logic that detects when the count is 9 and then resets the flip-flops on the next clock cycle. This can be done using an AND gate that takes inputs from Q3 and Q0 (1001) and outputs a signal to reset the counter.
With such a setup, a decade counter using D flip-flops would effectively count from 0 to 9 in binary form and then repeat the sequence.