# Synchronous Sequential Circuits in Digital Logic

Steps to solve a problem:**1.** Draw the state diagram from the problem statement or from the given state table.

**Example:** Serial Adder.

The functioning of serial adder can be depicted by the following state diagram. X1 and X2 are inputs, A and B are states representing carry.

**2.** Draw the state table. If there is any redundant state then reduce the state table.**3.** Select **state assignment** i.e. assign binary numbers to the states according to total number states. Also decide the memory element (flip-flops) for the circuit.

A -> 0

B -> 1**4.** Replace the assignments in the state table to obtain Transition table:**5.** Separate the output table from the transition table.

z = x_{1}x’_{2}y+x’_{1}x_{2}y’+x_{1}x_{2}y+x_{1}x’_{2}y’

**6.**Excitation table for the flip-flop is obtained from the transition table using the output of flip-flop.

**Excitation table for D flip-flop:**

D = x_{1} x_{2} +x_{1} y+x_{2} y

**7.**Draw the circuit diagram using gates and flip-flops.

This article is contributed by

**Kriti Kushwaha**

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