Base NumberDate: 10/07/98 at 18:11:41 From: steve Subject: Base Number? What does base number mean? I know we have a base 10 system and I think it has to do with when the numbers switch to two digits, but I know I'm wrong. Thanks. Date: 10/08/98 at 12:02:22 From: Doctor Peterson Subject: Re: Base Number? Hi, Steve. You have the general idea. A nice way to think of it is to look inside a counter, like the odometer in a car or the counter on some tape recorders, with a wheel for each digit. Each wheel has ten digits, 0 through 9; when it turns past 9 back to 0, it turns the wheel to its left one place, meaning "we've just counted ten more; I've started over at zero, so please keep track of the number of tens for me." Then that "tens" wheel counts until it turns back to zero, and it tells the next wheel to count one more set of 100, or 10 tens. Another way to think of it is that we count things by grouping them into stacks of ten, then stacks of ten into stacks of ten tens, and so on. When we write "123" it means we have one stack of 100, two stacks of 10, and three single items. You can do the same with other bases besides ten. If we had only two fingers instead of ten, we might be counting in base two -- that's what computers do! (In fact, the word "digit" originally meant "finger.") Here is our FAQ with links to more answers in our archives about different bases: http://mathforum.org/dr.math/faq/faq.bases.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 10/08/98 at 15:51:29 From: Anonymous Subject: Re: Base Number? How do computers know what the numbers 1 and 0 mean? I understand how programmers do stuff now since I am one (kinda - I've programmed a calculator and one game), but how did they start? How could the computers just know 1 is an apple and 0 is no apples? It boggles the mind! Date: 10/09/98 at 09:18:08 From: Doctor Peterson Subject: Re: Base Number? Hi, Steve. Good question - did my mention of computers stimulate this thinking, or have you wondered about this for a long time? Computers don't exactly know what numbers (or words, or pictures) mean, they just "know" what to do with them. A transistor, which is the basic unit of a computer, is a switch that can be wired to respond to an input by either turning on or off. Wire them together the right way, and they can add numbers (with "on" representing 1 and "off" representing 0); wire the adders together the right way, and they can do just about anything. It's the programmer who decides that a 1 in a certain place should mean "apple" or "hit" or "beep"; and usually you have a programming language translated by a compiler or interpreter program to insulate you from the details. The computer just manipulates all those bits according to your plan, and what comes out means what you wanted it to mean - if you programmed it right! Date: 10/09/98 at 22:14:00 From: Anonymous Subject: Re: Base Number? I have wondered about all those things but I kept thinking of more as I typed! |
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