Part of Lesson Plan: B7- When Does 3 and 6 = 7- How Computers Calculate

Activity Overview / Details

What is Boolean Logic? Don’t let the funny name throw you, it’s just named after a guy named George Boole.

 I have attached a video of the life of George Boolebelow if you want to show it.

George Boole was a mathematician who studied logic. He studied the concept of “syllogisms” which were first defined by the ancient Greek philosopher Socrates. Syllogisms were ways to see how different thoughts or sentences related to each other. For example, Socrates best known syllogism looked like this:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

Ask your students if they have heard any other syllogisms. Most students have at some point of their education. If you have time, have the students make up their own syllogism.

Syllogisms try to understand the relationship between several logical statements. In Socrates’ example, the question is, if the first statement is true and the second statement is true, does that mean the last statement is true? George Boole tried to take these philosophical concepts and turn them into mathematical formulas. He succeeded extremely well and a hundred years later, his works became the backbone of all current computer theory. Unfortunately, George Boole lived and died in a time long before computers, so in his lifetime he was seen more as a geeky nerd than anything else. Decades later people would rediscover his work and use it to design computer systems.

The basic parts of Boole’s work are called Boolean Logic or Boolean Algebra and focus mostly on three words, AND, OR and NOT. These words would be used to combine true and false statements together and then see if the resulting statement is overall true or false. For example, take the statement:

England is a country AND London is a city.

The first statement, “England is a country” is true and the second statement “London is a city” is true. When I combine these two statements together with the Boolean AND, they must both be true for the entire sentence to be true. In this case, we would say the sentence is true. But if we made the statement:

Elvis Presley was a singer AND Bill Gates is poor.

The first statement is true, but the second statement is false. Therefore, the entire sentence as a whole is false, even though the first part was true.

The Boolean word OR (or operators, as they are called) works similarly to AND except for OR, if either statement is true, the overall sentence is true. So in the case of the previous sentence about Elvis Presley and Bill Gates, the overall statement is true, even though the part about Bill Gates is false. The Elvis Presley statement makes it true, since only one OR the other statement has to be true to make the entire sentence true.

NOT is the simplest Boolean operator of all. All NOT does is reverse the value of a statement. A true statement becomes false and a false statement becomes true. So, for example, the statement “Bill Gates is poor” becomes “Bill Gates is NOT poor.” NOT does not need two statements to compare.

So how does this work with electronics? It turns out that if you use these concepts with electricity and consider “on” as “true” and “off” as “false”, Boolean logic works very well with circuits. Show these three videos:

Logic Gates- The AND Gate
Logic Gates- The OR Gate
Logic Gates- The NOT Gate

For a “quick and  dirty” presentation of the subject, you can use these short clips:

AND gate
OR gate
NOT gate

Boolean logic worked well with electronics, but when the computer was invented, it really found its place. It turns out that the transistor, which is the basis of computer technology, uses Boolean logic entirely. If you think of bits as little statements where a “one” bit is like a “true” statement and a “zero” bit is a “false” statement, transistors use Boolean logic to work with them. Here’s how it works:

AND:
1 + 1 = 1
1 + 0 = 0
0 + 1 = 0
0 + 0 = 0

OR:
1 + 1 = 1
1 + 0 = 1
0 + 1 = 1
0 + 0 = 0

You can see more of this process here:
http://computer.howstuffworks.com/boolean.htm