Code_ The Hidden Language of Computer Hardware and Software - Charles Petzold [39]
To begin your experiment, you connect a lightbulb and battery as you would normally, but you use two switches instead of one:
Switches connected in this way—one right after the other—are said to be wired in series. If you close the left switch, nothing happens:
Similarly, if you leave the left switch open and close the right switch, nothing happens. The lightbulb lights up only if both the left switch and the right switch are closed, as shown on the next page.
The key word here is and. Both the left switch and the right switch must be closed for the current to flow through the circuit.
This circuit is performing a little exercise in logic. In effect, the lightbulb is answering the question "Are both switches closed?" We can summarize the workings of this circuit in the following table:
Left Switch
Right Switch
Lightbulb
Open
Open
Not lit
Open
Closed
Not lit
Closed
Open
Not lit
Closed
Closed
Lit
In the preceding chapter, we saw how binary digits, or bits, can represent information—everything from numbers to the direction of Roger Ebert's thumb. We were able to say that a 0 bit means "Ebert's thumb points down" and a 1 bit means "Ebert's thumb points up." A switch has two positions, so it can represent a bit. We can say that a 0 means "switch is open" and a 1 means "switch is closed." A lightbulb has two states; hence it too can represent a bit. We can say that a 0 means "lightbulb is not lit" and a 1 means "lightbulb is lit." Now we simply rewrite the table:
Left Switch
Right Switch
Lightbulb
0
0
0
0
1
0
1
0
0
1
1
1
Notice that if we swap the left switch and the right switch, the results are the same. We really don't have to identify which switch is which. So the table can be rewritten to resemble the AND and OR tables that were shown earlier:
Switches in Series
0
1
0
0
0
1
0
1
And indeed, this is the same as the AND table. Check it out:
AND
0
1
0
0
0
1
0
1
This simple circuit is actually performing an AND operation in Boolean algebra.
Now try connecting the two switches a little differently:
These switches are said to be connected in parallel. The difference between this and the preceding connection is that this lightbulb will light if you close the top switch:
or close the bottom switch:
or close both switches:
The lightbulb lights if the top switch or the bottom switch is closed. The key word here is or.
Again, the circuit is performing an exercise in logic. The lightbulb answers the question, "Is either switch closed?" The following table summarizes how this circuit works:
Left Switch
Right Switch
Lightbulb
Open
Open
Not lit
Open
Closed
Lit
Closed
Open
Lit
Closed
Closed
Lit
Again, using 0 to mean an open switch or an unlit lightbulb and 1 to mean a closed switch or a lit lightbulb, this table can be rewritten this way:
Left Switch
Right Switch
Lightbulb
0
0
0
0
1
1
1
0
1
1
1
1
Again it doesn't matter if the two switches are swapped, so the table can also be rewritten like this:
Switches in Parallel
0
1
0
0
1
1
1
1
And you've probably already guessed that this is the same as the Boolean OR:
OR
0
1
0
0
1
1
1
1
which means that two switches in parallel are performing the equivalent of a Boolean OR operation.
When you originally entered the pet shop, you told the salesperson, "I want a male cat, neutered, either white or tan; or a female cat, neutered, any color but white; or I'll take any cat you have as long as it's black," and the salesperson developed this expression:
(M x N x (W + T)) + (F x N x (1 – W)) + B
Now that you know that two switches wired in series perform a logical AND (which