Sequential Circuits
The digital systems that have been defined and implemented in the preceding chapters are combinational circuits. If the component delays are not taken into account, that means that the value of their output signals only depends on the values of their inpu
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Sequential Circuits
The digital systems that have been defined and implemented in the preceding chapters are combinational circuits. If the component delays are not taken into account, that means that the value of their output signals only depends on the values of their input signals at the same time. However, many digital system specifications cannot be implemented by combinational circuits because the value of an output signal could be a function of not only the value of the input signals at the same time, but also the value of the input signals at preceding times.
4.1
Introductory Example
Consider the vehicle access control system of Fig. 4.1. It consists of • • • •
A gate that can be raised and lowered by a motor A push button to request the access Two sensors that detect two particular gate positions (upper and lower) A sensor that detects the presence of a vehicle within the gate area The motor control system has four binary input signals:
• • • •
Request equal to 1 when there is an entrance request (push button) Lower equal to 1 when the gate has been completely lowered Upper equal to 1 when the gate has been completely raised Vehicle equal to 1 if there is a vehicle within the gate area The binary output signals on/off and up/down control the motor:
• To raise the gate on/off ¼ 1 and up/down ¼ 1 • To lower the gate on/off ¼ 1 and up/down ¼ 0 • To maintain the gate open or closed on/off ¼ 0 The motor control system cannot be implemented by a combinational circuit. As an example, if at some time request ¼ 0, vehicle ¼ 0, upper ¼ 0, and lower ¼ 0, this set of input signal values could # Springer International Publishing Switzerland 2017 J.-P. Deschamps et al., Digital Systems, DOI 10.1007/978-3-319-41198-9_4
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request
Sequential Circuits
motor ON/OFF
request vehicle upper
motor control
UP/DOWN
lower
gate area
Fig. 4.1 Vehicle access control
correspond to two different situations: (1) a vehicle is present in front of the gate, the request button has been pushed and released, and the gate is moving up, or (2) a vehicle has got in and the gate is moving down. In the first case on/off ¼ 1 and up/down ¼ 1; in the second case on/off ¼ 1 and up/ down ¼ 0. In conclusion, the values of the signals that control the motor depend on the following sequence of events: 1. 2. 3. 4. 5. 6.
Wait for request ¼ 1 (entrance request) Raise the gate Wait for upper ¼ 1 (gate completely open) Wait for vehicle ¼ 0 (gate area cleared) Lower the gate Wait for lower ¼ 1 (gate completely closed)
A new entrance request is not attended until this sequence of events is completed. Conclusion: Some type of memory is necessary in order to store the current step number (1–6) within the sequence of events.
4.2
Definition
Sequential circuits are digital systems with memory. They implement systems whose output signal values depend on the input signal values at times t (the current time), t 1, t 2, and so on (the precise meaning of t 1, t 2, etc. will be defined later). Two simple examples are sequence detector
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