This section begins our study of designing an important class of clocked sequential logic circuits-synchronous finite-state machines.

**DESIGN OF SYNCHRONOUS COUNTERS:**

This section begins our study of designing an important class of clocked sequential logic circuits-synchronous finite-state machines. Like all sequential circuits, a finite-state machine determines its outputs and its next state from its current inputs and current state. A synchronous finite state machine changes state only on the clocking event.

Describe a general sequential circuit in terms of its basic parts and its input and outputs. Develop a state diagram for a given sequence. Develop a next-state table for a specific counter sequence. Create a FF transition table. Use K-map to derive the logic equations. Implement a counter to produce a specified sequence of states.

**Step 1: State Diagram**

State Diagram for a 3-bit Gray code counter:

**Step 2: Next-State Table**

Next state table for a 3-bit Gray code counter

**Step 3: Flip-Flop Transition Table**

Transition table for a J-K Flip-Flop

**Step 4: Karnaugh Maps**

The following diagram shows the steps to create separate next states of separate J and K from the current states of J and K.

Karnaugh maps for present-state J and K inputs for the 3-bit Gray code counter..

**Step 5: Logic Expressions for Flip-flop Inputs**

The next-state J and K outputs for a 3-bit Gray code counter.

**Step 6: Counter Implementation**

The hardware diagram of the 3-bit Gray code counter

**1.** **Design – Example 1**

Design a counter with the irregular binary count sequence shown in the state diagram of Figure 4.1.

**Step 1: State Diagram**

**Step 2: Next-State Table**

**Step 3: Flip-Flop Transition Table**

Transition table for a J-K Flip-Flop

**Step 4: Karnaugh Maps**

**Step 5: Logic Expressions for Flip-flop Inputs**

The expression for each *J* and *K* input taken from the maps is as follows:

J0 = 1, K0 = Q2

J1 = K1 = 1

J2 = K2 = Q1

**Step 6: Counter Implementation**

**Example 2 - Design the 3 Up/down counter (Gray code sequence)**

**Step 1: State Diagram**

**Step 2: Next-State Table**

**Step 3: Flip-Flop Transition Table**

Transition table for a J-K Flip-Flop

Here X denotes the don’t care condition Qn is the present state of transition output and

Qn+1 is the next state of the transition output

**Step 4: Karnaugh Maps**

**Step 5: Logic Expressions for Flip-flop Inputs**

**Step 6: Counter Implementation**

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Digital Electronics : Sequential Circuits : Design of Synchronous Counters |

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