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A synchronous sequential circuit with two D flip-flops (a,b as outputs), one input (x), and an output (y) is expressed by the following equations:

D_{a} = ab̅x + a̅b, D_{b} = x̅b + b̅x

y = b̅x̅ + a

(a) Derive the state table and state diagram for the circuit.

(b) Draw a logic diagram.

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