For

You are beginning an exciting journey as you prepare for the teaching profession. In your role as a teacher, you have to understand what a computer can do, and be able to use the computer to perform different tasks. A professional is not only knowledgeable, but is able to apply the knowledge. As a professional person, you must be prepared to expand your horizons. You are not merely trained to do a specific task.

Your primary task as a teacher is to educate. You can not educate without knowledge. One misconception, particularly in the computer world, is that knowledge becomes obsolete. This is false: knowledge does not go out of date. If you really learn the principles, then what you have learned assists you in learning new ideas. Certainly the computer technology improves, but what you learn today will help you understand the new developments tomorrow. You won’t be starting over from the beginning.

Don’t ever be of the opinion that you "don’t need to know much about computers". You are preparing to be an educator. You should want to know everything you can about everything. Your students will readily pick up your attitude and enthusiasm for learning. You certainly don’t want to close your mind, and, even worse, you don’t want to impart a negative attitude toward learning to your students. When someone tells you that you "really don’t need to know" something, run the other way! They are trying to control your thinking. By the same token, you want your students to have inquiring minds. Don’t turn them off by restricting what they learn.

The best computer is the human mind. No computer ever built ever did any thinking. The computer carries out the steps that it is instructed by you to do. Think of the computer as an extension of your mind in the same way that a sledgehammer is an extension of your arm. The sledgehammer extends the force of your arm and allows you do a task such as breaking up a big rock. The computer extends what originates in your mind. It allows you to do tasks that would take many hours of time to do with a pencil and paper.

Please understand that the computer did not spring up overnight. The ideas for the computer go back to the 1800’s. Neither does computing exist in a vacuum. As you proceed on your journey, you will find more and more areas that are related to the computer.

As a teacher, you will have many administrative duties. You need to keep records about your students. You need to communicate with parents. You need to know how to do word processing, how to do a spreadsheet, and how to maintain a database. While there are many different software packages that do these functions, by learning how to use a specific package you will be able to adapt to whatever package you may have available.

You may think of the computer as a collection of switching circuits. Now you have dealt with a switching circuit every time you turn on or turn off a light. The light has two states: on or off. The circuits inside the computer have only these two states. We designate off as zero and on as one. Thus, the computer has only these digits to work with: 0 and 1. You are far more advanced than this. Since your early childhood you worked with the following digits: 0,1,2,3,4,5,6 7,8,9. The system you worked with is known as the decimal system. Why do you suppose you work with a system that has ten digits? (Hint: Had man invented the rotary power lawnmower before he developed the numeration system, we might have a system based on nine digits.) Yes, the decimal system developed because humans have ten fingers.

Well, the computer does not have fingers. All the computer has is switching circuits. Each circuit is either off (zero) or on (one). Could you do arithmetic with only the digits 0 and 1?

To answer this question, think about the odometer on an automobile or bicycle. This device counts the distance that the vehicle has traveled in miles (or kilometers). Each wheel of the odometer has ten digits. If you take delivery of a brand new vehicle, the odometer might appear as shown below:

After you have traveled one mile, the odometer would appear as follows:

After nine miles, the odometer shows the following:

What happens after you travel the next mile (besides the warranty expiring)? The wheel on the right has made one complete revolution. The next wheel to the left then rotates to a 1. The odometer then appears as shown below:

After you have traveled nineteen miles, the odometer appears as follows:

When you travel the next mile, the first wheel on the right has made two revolutions. The next wheel to the left is then bumped to the next digit and the odometer shows the following:

Now imagine an odometer that has only two digits on each wheel: 0 and 1. Let’s count miles in this system. (This system is called the binary system. Remember that "bi" means two). Suppose that the new vehicle you have just purchased counts miles in binary. When you take delivery of the new vehicle, the odometer appears as follows:

When you have driven the vehicle one mile, the odometer reads as follows:

Now you put the second mile on the vehicle. At this point, the right wheel has made one complete revolution (remember, this wheel has only two digits: 0 and 1). The second wheel from the right is advanced one digit. Thus, two miles is recorded as follows:

After three miles, the odometer looks like this:

When the vehicle has racked up the fourth mile, the right wheel returns to zero. This then moves the second wheel from the right one digit. It, too, becomes a zero. Since it has made a complete revolution, the third wheel from the right is moved one digit. The new reading is:

Counting in binary is the same process as counting in decimal. Examine the comparison between the two numeration systems:

Number Binary Decimal

Zero 0 0

One 1 1

Two 10 2

Three 11 3

Four 100 4

Five 101 5

Six 110 6

Seven 111 7

Eight 1000 8

Nine 1001 9

Ten 1010 10

Eleven 1011 11

Twelve 1100 12

Thirteen 1101 13

Fourteen 1110 14

Fifteen 1111 15

Sixteen, represented in binary, would be 10000. How high could one count in binary? You could keep counting forever, just as you did in the decimal system. If counting in binary gives you trouble, just imagine an odometer with only the two digits, 0 and 1, on each wheel.

You grew up with the decimal system. We have examined the binary system. Of course, there are other numeration systems. One system that is used in computing is the hexadecimal system. "Hex" means six and "dec" means ten. Therefore, when we are referring to the hexadecimal system, we are referring to a system with six plus ten or sixteen digits. You are used to the ten digits: 0,1,2,3,4,5,6,7,8,9. You need six more digits. Engineers, in their unimaginative way, solved this problem by using the letters A, B, C, D, E, and F to represent the remaining digits. Therefore, the digits in the hexadecimal system are the following:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

You can count in the hexadecimal system as well. This time, imagine an odometer with sixteen digits on each wheel. Starting with zero, you would count as follows:

0,1,2,3,4,5,6,7,8,9,A, B, C, D, E, F, 10,11,12,13,14,15,16,17,19,19,1A, 1B, 1C,1D,1E,1F,20,21 . . .

In the mathematics courses you take, you will study different numeration systems in more depth. Just remember that mankind’s choice of the decimal system was very arbitrary. It came into existence because humans have ten fingers.