Please solve this digital logic design question
Q4) A sequential circuit with two T flip-flops, A and B is described by the following flip-flop input equations:
TA=A'B
T.=A'+B'
(a) Draw the logic diagram of the circuit.
(b) List the state table for the sequential circuit.
(c) Draw the corresponding state diagram.

Question

Accepted Answer

⚹ Based on the OCR model's understanding, there seems to be a discrepancy in the equations provided for the T flip-flops A and B. The understanding mentions $T_A = A'B'$ and $T_B = A + B$, while the text from Img 1 states $T_A = A'B$ and $T_B = A' + B'$. Assuming the text from Img 1 is correct, I will proceed with the solution. ⚹ (a) ⚹ To draw the logic diagram of the circuit, you will need two T flip-flops, one for A and one for B. The input to flip-flop A, $T_A$, is the output of an AND gate with inputs $A'$ and $B$. The input to flip-flop B, $T_B$, is the output of an OR gate with inputs $A'$ and $B'$. Connect the outputs of the flip-flops back to the inputs as needed for the feedback. ⚹ (b) ⚹ The state table for the sequential circuit can be listed as follows: | Current State (AB) | Next State (AB) | $T_A$ | $T_B$ | |--------------------|-----------------|-------|-------| | 00 | 01 | 0 | 1 | | 01 | 11 | 1 | 1 | | 11 | 10 | 0 | 0 | | 10 | 00 | 1 | 1 | The next state is determined by the current state and the input equations for $T_A$ and $T_B$. ⚹ (c) ⚹ The corresponding state diagram can be represented as a 5-tuple formal definition in LaTeX: A deterministic finite automaton (DFA) can be represented as a 5-tuple $(Q, \Sigma, \delta, q_0, F)$, where: - $Q$ is a finite set of states. - $\Sigma$ is a finite input alphabet. - $\delta: Q imes \Sigma ightarrow Q$ is the transition function. - $q_0 \in Q$ is the start state. - $F \subseteq Q$ is the set of accept states. For the given sequential circuit, the DFA can be defined as: - $Q = \{00, 01, 11, 10\}$ - $\Sigma = \{T_A, T_B\}$ - $\delta$ is defined by the state transitions. - $q_0 = 00$ (assuming the initial state is 00) - $F$ is not specified as it's not a part of the problem. The LaTeX code for the state diagram is as follows: ```⚹latex \documentclass{standalone} \usepackage{tikz} \usetikzlibrary{automata, positioning, arrows} \begin{document} \begin{tikzpicture}[->, >=stealth', auto, semithick, node distance=3cm] ikzstyle{every state}=[fill=white,draw=black,text=black] ode[state,initial] (00) {$00$}; ode[state] (01) [above right of=00] {$01$}; ode[state] (11) [below right of=01] {$11$}; ode[state] (10) [below right of=00] {$10$}; \path (00) edge[bend left] node{$T_B$} (01) (01) edge[bend left] node{$T_A, T_B$} (11) (11) edge[bend left] node{} (10) (10) edge[bend left] node{$T_A, T_B$} (00); \end{tikzpicture} \end{document} ``` ⚹ Since the graph contains only four states, the LaTeX code provided should be sufficient to generate the graph. However, if the graph were more complex, it would be advisable for the student to draw it themselves, referring to the explanation above. ⚹

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