Combinational Circuits vs. Sequential Circuits

Instructor: Shadi Aljendi

Shadi has a Ph.D. in Computer Science and more than 20 years experience in industry and higher education.

In this lesson we will learn some basics of sequential circuits and the main characteristics that differentiate them from combinational circuits. We will address the two main concepts that sequential circuits implement: memory and time. We will also cover the basic aspects of state and clock.

Introduction

Digital logic circuits can be classified into two types: combinational and sequential. Combinational circuits are logic circuits in which their outputs depend only on their inputs. Combinational circuits are often known as time-independent and stateless circuits. On the other hand, the outputs of sequential circuits depend not only on their inputs, but also on the state of the circuit.

In order to understand the difference between combinational and sequential circuits, let us assume that you want to design a circuit that counts the number of people entering a room. How would you do this? Would you be able to build this as a combinational circuit?

In order to answer this question, let us outline how a counter would work. In order for a system to be able to count events, it needs to do two main things:

  • It needs to be able to remember the last number reached.
  • It needs be able to recognize two successive events with a time lapse between them

Thus, in order to design a counter, we need to 'implement' two circuit characteristics: memory and time. These two aspects are not easily implemented using combinational logic.

The State of a Sequential Circuit

Unlike combinational circuits, the output of a sequential circuit depends not only on its inputs, but also on its state. State can be defined as a condition that an entity is in at a particular time. Notice that in this definition, not only the word is 'time' used, but also the word 'particular'. This indicates that the condition is stable or fixed at a point in time.

Memory in Sequential Circuits

Because digital circuits process binary data, the 'condition' or the state of the circuit will consist of nothing more than binary data. For stability and recall, we need to store this data in memory. In other words, memory cells are required for sequential circuit implementation and represent the state of the circuit. This state might or might not be part of the circuit's output, however.

In our counter example mentioned above, the state of the counter would be the count. If 4 people had already entered the room, the state of the counter would be 100 in binary (or 4). The three binary bits (1, 0 and 0) are stored in memory cells called flip-flops.

This helps us understand why the output of a sequential circuit not only depends on the input but also on the state of the circuit. If the current state of our counter is 4, and a person enters the room then the new output (state) will be 5. If yet another person enters, the current state will be 5 and the new output (state) will be 6. Notice that in both cases the input of the circuit is the same event: a person enters the room.

Time in Sequential Circuits

Now that we've talked about memory in sequential circuits, we need to now understand how they implement the concept of time. In order to do this, sequential circuits must be built as event-driven entities. When an event takes place, a sequential circuit will trigger a state change. In our counter example, the event will be a person entering the room, and the triggered reaction of the circuit will be to increment its count by 1.

The question now is: How does the circuit 'detect' the event? The answer is that the event must be transformed into an electronic signal and sent to the circuit as an input. The most commonly used triggering signal in sequential circuit logic is the square wave.

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