東京大学情報理工学系研究科電子情報学専攻 2024年度専門第2問

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Consider designing a binary digital synchronous sequential circuit as follows.

The circuit has \(2\) inputs \((X_1,X_0)\) and \(1\) output \((Z)\).
The inputs \((X_1,X_0)\) represent a character from \(A\) to \(D\) encoded as \(A = (0,0), B = (0,1) , C = (1,0)\) , and \(D = (1,1)\).
The output \(Z\) is \(1\) when the last two consecutive inputs are \(AA , AC , CB , CD , DA ,\) or \(DC\); otherwise \(Z\) is \(0\).

Answer the following questions.

(1) Explain in \(50\) words or less what a synchronous sequential circuit is.

(2) Draw a state transition diagram of the circuit in the form of a Mealy graph. Use \(4\) states corresponding to each character. Each state represents that the corresponding character is the last input.

(3) The output \(Z\) must be \(0\) until the first two characters are given as inputs to the circuit. Answer which state in the state transition diagram in (2) should be the initial state to achieve this.

(4) Simplify the state transition diagram in (2) so that it has \(3\) states.

(5) Create a state transition table from the state transition diagram in (4).

(6) Draw Karnaugh maps from the state transition table in (5).

(7) Simplify the logic as much as possible using the Karnaugh maps in (6), and draw the circuit using MIL simbols shown in the Fig.