Computer Basics Tutorial Number 1
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How do computers store information?

Computers store information by using switches (on-off switches, like the ones used for turning on/off lights, except a lot smaller, and implemented with electronics - i.e. no moving parts).

It works like this. Suppose you want to store some information. You go down to the hardware store and buy a switch. OK, now you have a binary digital storage device. "Digital" means basically that it only can have one of a set number of possible states, and "binary" means that it can only have two such possible states. That is, it can be either on or off. An example of a device that is neither binary nor digital would be a slide rule. Slide rules have an infinite number of possible states, and such devices are called "analog" as opposed to "digital".

So far so good. You have a binary digital storage device. Now you just have to decide how to represent information on it. You have two possible states you can use, which means you can "store" two pieces of information by specifying a "code".

Let's use numbers to represent the possible states of the switch. "0" means the switch is off (up) and "1" means it is down. So let's make a weather code.

0 = it's raining
1 = it's not

So now you have a personal digital assistant which stores the day's weather report. So that's pretty cool, and you go out to show it to your friend. You meet your friend, and pull out your switch and look at it (information retrieval), remember the code (information processing) and say, "look, according to my PDA, it is raining".

Your friend says, "that's nice...but as a matter of fact it stopped raining an hour ago". And then she pulls out her PDA and shows you how she has the very same info, plus a copy of War and Peace, stock market quotes, and a complete mirror of "alt.liberal.arts.disgruntled".  That's because your friend's PDA has about 100 million more switches than yours.

So you are pretty crestfallen, and go back to the hardware store and ask if they have 100 million switches in stock. They don't, they only have 23. But that's a start, so you buy them and go back to your living room, where you try to assemble them into a more powerful PDA.

Now you have 23 switches. How can you store more information? Well, since you have more switches, your PDA can have more possible states. For example, suppose you take two switches and put them side by side. Now, instead of two possible states, you have four:

00
01
10
11

This is looking promising, so you put another switch alongside the other two:

000
001
010
011
100
101
110
111

Now you have 8 possible combinations. If you think of it, every time you add another switch, you are doubling the number of possible combinations, thus doubling the amount of "information" you can hold. I put "information" in quotes because it isn't really information until you specify what these combinations are supposed to mean, in other words you need a code (keep reading).

So, if you have n switches you have 2**n possible combinations.

By the way, if you want to know why I ordered the combinations above the way that I did, the answer is, I was counting in binary, that is, base 2. Counting in base 2 is just like counting in decimal, except that each step to the left is another power of two, instead of a power of 10.

(You'll have a happier, longer, more fulfilling life if you stop right now, take out a pencil, and mess around with binary numbers a bit until you get the hang of them. Try converting some binary numbers to decimal and vice versa. Play around with a binary counter: Binary Counter #1 - Binary Counter #2 - Binary Counter #3 - Binary Counter #4 - Binary Counter #5)

OK, let's line up our 23 switches and start storing some information. We have 2**23 possible combinations, which is ... a lot.

00000000000000000000000 = "it's not raining"
00000000000000000000001 = "it's raining"
00000000000000000000010 = "the capital of the USA is New York City"
00000000000000000000011 = "disregard the statement in the previous record, it is incorrect, although some people don't know that".

This could start getting out of hand.... Let's try something else: how about just making a code for letters, and then storing only letters? It will make our code a lot simpler, for one thing.

If we are going to store letters, we don't need to use all 23 switches for a single letter. We wouldn't want to use all of our switches for a single letter anyway, because then we can only store 1 letter in our PDA.

What's the minimum number of switches we need to store letters?
Let's see:
1 switch = 2 possible combinations
2 switches = 4 possible combinations
3 switches = 8 possible combinations
4 switches = 16 possible combinations
5 switches = 32 possible combinations
6 switches = 64 possible combinations
7 switches = 128 possible combinations
8 switches = 256 possible combinations

5 switches is enough for 26 letters, but then we can't specify upper/lower case. Plus we want to specify digits (1,2,3 etc.) and punctuation too.
So we need at least 7 switches. We don't need more than that. We can arrange the switches in groups of 7, and then can start storing information by putting the code for a letter or other symbol in each 7-switch group.

Now, if we are going to make a code, it would be best if we also agree with others on this code, that is, make it a convention. That way, we can share devices (hardware) and information (software).

Better yet, check to see if someone has already made a code. Someone has, it is called "ASCII". ASCII is a code made up by a group of computer companies and industry representatives. They made an 8-switch code, probably because grouping by 8 is a lot easier than grouping by 7, since 8 is an even number. They used the extra switch for error checking. (This particular error checking is called "parity" and is used when transferring bytes between computers. That is done not by picking up the switch and throwing to the other computer, (although that would work too), but by attaching a wire between the computers and sending "0"s and "1"s by means of an electronic signal. Sometimes the signal gets messed up in transit, and that is where error checking comes in. But more on that in a later tutorial.)

By the way, people don't usually talk about switches and switch groups when talking about computers, because it is more usual to think in terms of information than in terms of hardware. One switch can store one "bit" of information. So, one 0-1 unit is called a "bit". 8 bits is called a "byte". It is called a "byte" because someone thought that "byte" was a cute name for a bunch of "bits".

You can see the complete ASCII code here.

The ASCII table above has an entry for the binary "number", the equivalent decimal number, and the character that the code is representing. There is also a column entitled "hex", for hexidecimal. Hexidecimal is base 16.

Counting in base 16 goes like this:
HEX 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 22
DEC 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

Why is base 16 useful? First, let's consider why no one likes to work directly with binary numbers. The problem with using binary is obvious, the numbers can be very long and hard to work with. Decimal is what we are all familiar with, and that is best EXCEPT it is a pain to convert between binary and decimal. Try converting the following to decimal.

001100101101001001101011101010111000110

Quick! What's the answer?

I'm sorry that is incorrect. Please check your answer. And try to be more careful.

Oh really? My mistake.

OK, how about converting this to binary?

345,663

Yes, I agree, let's just forget about that one.

But converting back and forth between hex and binary is a breeze, and it is even more compact than decimal. The reason hex is so easy is that 4 bits gives you 16 possible combinations, and hex has exactly 16 different digits (just as decimal has exactly 10 different digits: 0,1,2,3,4,5,6,7,8, and 9). That means hex "lines up" with the bits - you have one hex digit for every 4 bits. All you have to do is memorize converting binary-to-hex from 1 to 16, and then you can easily convert arbitrarily long binary numbers. Like this:

bin = 0001 0010 1111 1100 1010 0110 0010 1111
hex = 124FCA52F

BIN
0001
0010
0100
1111
1100
1010
0110
0010
1111
HEX
1
2
4
F
C
A
6
2
F

For this reason, programmers usually use hex when they are working directly with binary values.

But, IP addresses (the numbers that TCP-IP uses to identify a computer) are in decimal form for some reason, even though one frequently has to convert back and forth between binary and decimal values. It would have been a lot simpler if they had been in hex...

To be continued....



Extended ASCII.

Double byte codes

CPU calculations.

AND, OR, NOT

Transistors. (Vacuum tubes)



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