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Questions and Answers
What is the first step in designing a synchronous counter?
What is the first step in designing a synchronous counter?
State Diagram
What does the next-state table list?
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?
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?
How are Karnaugh maps used in designing synchronous counters?
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What do you obtain from Karnaugh maps in step 5?
What do you obtain from Karnaugh maps in step 5?
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What is the final step in the design of a synchronous counter?
What is the final step in the design of a synchronous counter?
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A state diagram shows the inputs and outputs of the counter.
A state diagram shows the inputs and outputs of the counter.
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The least significant bit in a 3-bit Gray code counter is represented as Q______.
The least significant bit in a 3-bit Gray code counter is represented as Q______.
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Which of the following is NOT a step in designing a synchronous counter?
Which of the following is NOT a step in designing a synchronous counter?
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Match the following stages of counter design with their descriptions:
Match the following stages of counter design with their descriptions:
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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.
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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.
