CYBER NOTES by Dave Benore
Do computers make mistakes?
No! I guess that takes some explanation. 99.99999….% of all computer ”mistakes” are really operator error. Someone input the wrong data into a computer—or put it into the wrong place (by bumping a keyboard key without realizing it). We do that at home too, don’t we?
So what about that tiniest fraction that is not operator error? Once in a v..e..r..y great while some electrical component in a computer might go bad. So how do you know? The mistakes a computer makes when a component goes bad are real whoppers! It’s like adding 2+2 and getting 90,328. There is no misunderstanding—the computer made a mistake. Or the letter you typed becomes gibberish. No misunderstanding there! Most of the time a component failure will stop the computer from running at all.
Many people don’t realize that every time you start your home computer up, or do a “cold” boot as it’s called, the computer goes through a self-diagnostic process which tests all of its components, including its RAM memory. If it finds a failure it refuses to boot up—to start. This process is called the “POST” (for power on self test).
(By the way, a “cold” boot is starting up a computer by turning the electrical power on. A “warm” boot is restarting a computer without first turning the electrical power off. RAM memory stands for random access memory. It is the memory your computer uses while running programs. It is not the hard disk. More on this in a coming article.)
So what makes a computer so accurate? It is a digital device operating mostly in the number system of base two. Well, what is that, exactly? Time to put your thinking cap on.
First the digital part. You’ve seen digital clocks and watches. They tell you the time by displaying digits—a digital display. There is no hand going around that you have to interpret against a background dial. The alternative is an analog display. That’s like a clock that has a hand moving around, or a speedometer in your car with a hand that points to the speed. So a display can be either digital or analog. But a display only shows you an answer. It does not calculate, or process information, to create the answer.
So the question totally separate from the display, is how electrical signals—which represent information--are processed internally within a device like a computer. There can be a great difference in the method of processing. That difference is really what makes a device digital or analog, not the display of the answer.
Analog devices use the exact value of voltage or current to represent information. But, they are subject to the introduction of small errors in voltage or current because of how electricity works.
But digital devices, using a different electrical process internally, are not subject to any of these errors. This is because digital devices do not care what the exact value of voltage or current is. They only care whether any voltage or current is present or absent. In other words, digital processing recognizes whether electricity is on or off--period. The exact value is immaterial. This certainty of recognizing one of two states, on or off, leads us to the number system of base 2.
Number system of base 2 Let’s start with what we know. We all use the decimal system in our lives. It has 10 characters; 0,1,2,3,……..9. This is a number system of base 10, our decimal system. (Deci means ten.) It most probably was created by ancient people who used their 10 fingers for counting stuff. It was “natural”. But it isn’t the only numbering system. In fact there can be an infinite number of numbering systems—each one with a different base.
Go back to the decimal system. In grade school we were taught that in writing numbers there was a units place, a tens place, a hundreds place, thousands, ten thousands, etc. And in each place we wrote the “number” of tens, hundreds, etc. by using the characters 0 through 9. For example, the number 4897 means that there are 4 “thousands” and (+) 8 “hundreds”, and 9 “tens”, and 7 “units”. For the mathematically inclined, that can be written: 4897 = 4x103 + 8x102 + 9x101 + 7x100. (In math, any number to the 0 power = 1) Notice how the powers of 10 change. (Whew! Makes my brain ache.) We have just defined the number system of base 10!
So, for base 2, we have only 2 characters, 0 and 1. Looks weird? It goes like this. There is a units place, and a twos place, and a fours place, and an eights place, a sixteens, a thirty-twos, etc. Numbers in this system are called binary. (Bi means two.) Take our decimal number 3. In binary that would be 11 (1unit + 1 two). Decimal 4 would be binary 100 and decimal 5 would be 101. Binary 101 = 1x22 + 0x21 + 1x20. We have just defined the binary number system!
Back to computers. Since digital processing in computers recognizes the presence or absence of electricity perfectly, why not let the presence of voltage = 1 and the absence = 0? Then all the little errors that plague analog systems have no effect. Voila!
We input numbers to the computer in the decimal system. The computer then converts them to binary numbers, does all its calculations in binary where there are no errors, then converts the answers back to decimal before sending them to the monitor or printer for us to see. And that’s why computers don’t make mistakes!
P.S. I’m sorry for all the technical stuff but I just don’t know how to explain it more simply. The truth is that computers are very technical. In fact, they also routinely use the number system of base 16, and sometimes base 8, for control purposes. How about them puppies!
