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When you turn the switch on, the first relay is triggered, which then provides a voltage to the second relay. The second relay is triggered and the light goes on:

Connecting relays is the key to building logic gates.

Actually, the lightbulb can be connected to the relay in two ways. Notice the flexible metal piece that's pulled by the electromagnet. At rest, it's touching one contact; when the electromagnet pulls it, it hits another contact. We've been using that lower contact as the output of the relay, but we could just as well use the upper contact. When we use this contact, the output of the relay is reversed and the lightbulb is on when the input switch is open:

And when the input switch is closed, the bulb goes out:

Using the terminology of switches, this type of relay is called a double-throw relay. It has two outputs that are electrically opposite—when one has a voltage, the other doesn't.

By the way, if you're having a tough time visualizing what modern relays look like, you can see a few in conveniently transparent packaging at your local Radio Shack. Some, like the heavy-duty relays with Radio Shack part numbers 275-206 and 275-214, are about the size of ice cubes. The insides are encased in a clear plastic shell, so you can see the electromagnet and the metal contacts. The circuits I'll be describing in this chapter and the next could be built using Radio Shack part number 275-240 relays, which are smaller (about the size of a Chiclet) and cheaper ($2.99 apiece).

Just as two switches can be connected in series, two relays can be connected in series:

The output of the top relay supplies a voltage to the second relay. As you can see, when both switches are open, the lightbulb isn't lit. We can try closing the top switch:

Still the lightbulb doesn't light because the bottom switch is still open and that relay isn't triggered. We can try opening the top switch and closing the bottom switch:

The lightbulb is still not lit. The current can't reach the lightbulb because the first relay isn't triggered. The only way to get the bulb to light up is to close both switches:

Now both relays are triggered, and current can flow between V, the lightbulb, and ground.

Like the two switches wired in series, these two relays are performing a little exercise in logic. The bulb lights up only if both relays are triggered. These two relays wired in series are known as an AND gate. To avoid excessive drawing, electrical engineers have a special symbol for an AND gate. That symbol looks like this:

This is the first of four basic logic gates. The AND gate has two inputs (at the left in this diagram) and one output (at the right). You'll often see the AND gate drawn as this one is with the inputs at the left and the output at the right. That's because people who are accustomed to reading from left to right also like to read electrical diagrams from left to right. But the AND gate can just as well be drawn with the inputs at the top, the right, or the bottom.

The original circuit with the two relays wired in series with two switches and a lightbulb looked like this:

Using the symbol for the AND gate, this same circuit looks like this:

Notice that this symbol for the AND gate not only takes the place of two relays wired in series, but it also implies that the top relay is connected to a voltage, and both relays are connected to ground. Again, the lightbulb lights up only if both the top switch and the bottom switch are closed. That's why it's called an AND gate.

The inputs of the AND gate don't necessarily have to be connected to switches, and the output doesn't necessarily have to be connected to a lightbulb. What we're really dealing with here are voltages at the inputs and a voltage at the output. For example, the output of one AND gate can be an input to a second AND gate, like this:

This bulb will light up only if all three switches are closed. Only if the top two switches are closed will the output of the first AND gate trigger the first relay in the second AND