MOORE FINITE STATE MACHINE: CONTROL CIRCUIT FOR
AUTOMATIC DOOR
by Isai Damier (Let's connect on twitter @isaidamier )

Problem Description for Control Circuit

Some time ago, I had a fictitious meeting with the representatives of a department store. They were planning to upgrade their chain of stores with automatic double doors that swing open, and so they hired me to build a circuit to control the automatic operation of the doors. They had two specific requirements. First, while opening, a door should not hit shoppers who happen to be standing behind the entrance. Second, when no one is around, the door should stay closed to save on air conditioning cost.

Requirement Analysis for Control Circuit

This problem is asking me to replace a doorman with a machine (a circuit to be exact). So instead of trying to come up with some fancy engineering solution, I go to a doorman and ask him to explain his work to me. He took a piece of napkin and a pencil and drew the picture in Figure 1 below.

Figure 1: Doorman Diagram

I asked him to explain the drawing and here is what he said: “ This is no rocket science. A door is either open or closed. So I draw two boxes and label one open and one closed. If the door is closed, I open it only when there are people in front of it but nobody to the REAR of it. So I draw an arrow from closed to open and label it front. In addition, the only time I close a door that's already open is when there is nobody around. So I draw another arrow from open to closed and label it neither. Under all other conditions, if the door is open it will stay open. And if the door is closed, it will stay closed. So I draw the two other arrows and label them with everything else. ”

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Clearly this doorman has an eye for details. My work is done. The doorman's schematic is all I need to build the circuit. Nevertheless, a good inventor never reveals his sources. Hence, in my official report I changed what the doorman told me so to sound high-tech. First, I labeled the drawing state transition diagram to make it sound sophisticated (see Figure 2 below). Second, I revised the doorman's explanation and wrote the following.

To read the state transition diagram in Figure 2, imagine the door has two floor pads -- a front pad and a rear pad -- and that the circuit controlling the door is listening to weight on the pads. Therefore, Neither means there is nobody on either pad; Front means there is someone on the front pad only; Rear means there is someone on the rear pad only; and Both means there are people on both pads.

Figure 2: State Transition Diagram

Of course I thanked the doorman for his pains and bought him lunch. I am a nice guy.

Designing the Control Circuit

In reality, the state diagram in Figure 1 is the solution to the problem. Once you have a state diagram, the rest is just techniques. Indeed there are many software applications right now that can print a working circuit from a state diagram. Therefore, it's very important to practice drawing state diagrams. Take a pencil and paper and try to draw the doorman's schematic from the description. Do not continue until you get the drawing right. You must think like the doorman. Be the doorman.

From the state diagram, you are four steps away from a working circuit.

1. Translate the state diagram to a table
2. Make the table look like K-maps
3. Get the Boolean expressions from the K-maps
4. Draw the circuit from the Boolean equations.

Step 4 is not really worth mentioning. But I add it for the sake of completeness.

Digital System Implementation Procedure

A technique is like a magic trick: It's impressive the first time you see it; but once you get the secret, it becomes a joke. Our first technique is to translate the state diagram in Figure 1 into a table. From the state diagram we see that the door can be in two possible states (open; closed); and movement from state to state is governed by four conditions (neither; front; rear; both). To construct the table, we will label the rows by states (i.e. closed; open). And we will label the columns by conditions (i.e. neither; front; rear; both). Figure 3 below is our empty table.

State	Conditions
	Neither	Front	Rear	Both
Closed
Open

Figure 3: Empty State Transition Table

Next we fill the table by following the arrows in the state diagram. For instance, the arrow that goes from closed to open is labeled front; which means if the door is closed and the condition is front then the door will go open. So in Figure 4, we write open in the cell where closed and front intersect.

State	Conditions
	Neither	Front	Rear	Both
Closed		Open
Open

Figure 4: State Transition Table with one cell

Figure 5 represents the completed state transition diagram. I add a few more labels to make the table easier to read. You should check Figure 5 against Figure 1 to make sure that the information match exactly.

Given state of door	Shopper location
	Neither	Front	Rear	Both
	What will happen to door (Next State)
Closed	Closed	Open	Closed	Closed
Open	Closed	Open	Open	Open

Figure 5: State Transition Table

Nearly all designers use this table. As a result, different people call the table by different names: state table, excitation table, flow table, state assigned table, etc. Whatever name you choose to call the table, make sure your audience knows what you are talking about.

Because the table represents the operation of a logic circuit, it makes sense to replace the states with 0s and 1s: Closed = 0; Open = 1. Hence, Figure 5 becomes Figure 6.

Given state of door	Shopper location
	Neither	Front	Rear	Both
	What will happen to door (Next State)
0	0	1	0	0
1	0	1	1	1

Figure 6: Excitation Table