Logic Circuits II – Lecture 7

Questions and Answers

What is the first step in designing a synchronous counter?

State Diagram

What does the next-state table list?

Each state of the counter and the corresponding next state.

What is the function of the flip-flop transition table?

It shows all possible output transitions of the flip-flop.

How are Karnaugh maps used in designing synchronous counters?

To determine the logic required for the J and K inputs of each flip-flop. Signup and view all the answers

What do you obtain from Karnaugh maps in step 5?

Logic expressions for flip-flop inputs. Signup and view all the answers

What is the final step in the design of a synchronous counter?

Counter Implementation Signup and view all the answers

A state diagram shows the inputs and outputs of the counter.

False Signup and view all the answers

The least significant bit in a 3-bit Gray code counter is represented as Q______.

0 Signup and view all the answers

Which of the following is NOT a step in designing a synchronous counter?

Determine the clock frequency Signup and view all the answers

Match the following stages of counter design with their descriptions:

Step 1 = State Diagram creation Step 2 = Next-state table derivation Step 3 = Transition table development Step 4 = Karnaugh map creations Step 5 = Logic expression derivation Step 6 = Counter implementation Signup and view all the answers

Study Notes

Design of Synchronous Counters

Designing a synchronous counter involves a sequence of six essential steps.
The process begins with a state diagram, illustrating the progress of states as the counter is clocked. A 3-bit Gray code counter serves as an example.

Next-State Table

The next-state table follows the state diagram, detailing the current state and its corresponding next state upon clock pulse application.
This table is crucial for understanding how each state transitions.

Flip-Flop Transition Table

A transition table for J-K flip-flops displays all potential output transitions, showing how the Q output changes from present to next state.
Present state (QN) and next state (QN + 1) identify the transitions needed; J and K inputs associated with those transitions are included.
An “X” signifies a “don’t care” condition, allowing flexibility in input assignments.

Karnaugh Maps

Karnaugh maps serve as a tool to derive logic for J and K inputs for each flip-flop.
Each cell represents a current state of the counter, with classifications of 1, 0, or X based on output transitions from the transition table.

Logic Expressions for Flip-Flop Inputs

From the Karnaugh maps, logic expressions for each flip-flop's J and K inputs are formulated, guiding the next phases of circuit design.

Counter Implementation

The final stage involves implementing combinational logic based on derived expressions to assemble the complete 3-bit Gray code counter.
Following the design steps guarantees proper construction of a synchronous counter, relevant for any type of state machine.

Description

Explore the design of synchronous counters in this lecture. Learn the six essential steps, starting with the creation of a state diagram to visualize state transitions. This foundational concept is crucial for designing efficient state machines.