Designing a Sequential Circuit with Specific Input Sequence
Introduction
A sequential circuit is a type of digital circuit that utilizes memory elements to store information about its history or past inputs. In this case, we are tasked with designing a sequential circuit that has one input and one output. The circuit should be able to identify a specific input sequence, in this case, "1001," and toggle the output accordingly. When the input sequence "1001" occurs, the output becomes 1 and remains 1 until the sequence "1001" occurs again, at which point the output returns to 0. This toggling behavior continues whenever the input sequence "1001" is received.
Designing the Sequential Circuit
To achieve the desired functionality, we can implement a Finite State Machine (FSM) in the sequential circuit. The FSM will have multiple states to keep track of the input sequence and determine the output based on the current state.
Key Steps:
- Determine the number of states required to track the input sequence.
- Create a state transition diagram that outlines how the circuit should move between states.
- Define the logic for the output based on the current state.
Explanation
When the input sequence "1001" is received, the FSM should change states and toggle the output accordingly. The circuit starts in an initial state (OFF) where the output is 0. Upon receiving the first "1001," the circuit moves to a new state (ON) and sets the output to 1. Subsequent occurrences of "1001" will transition the circuit through different states, toggling the output each time.
An example of a 4-state machine could represent this behavior:
- State 0: Initial state (Output 0)
- State 1: Received "1" (Output 0)
- State 2: Received "10" (Output 0)
- State 3: Received "100" (Output 0)
- Back to State 0: Received "1001" (Output 1)
The circuit will remain in the last state until the input sequence "1001" is detected again, causing the output to toggle back to 0. This behavior continues indefinitely as long as the input sequence "1001" repeats.
How can a Finite State Machine be utilized in designing a sequential circuit with specific input sequence toggling the output? A Finite State Machine is essential for designing a sequential circuit that can identify and respond to specific input sequences. By defining different states to track the input sequence progression and determining the output based on these states, the FSM enables the circuit to toggle the output as required. In this case, the FSM helps create a circuit that toggles the output whenever the input sequence "1001" is received, following a predefined pattern of state transitions.