An Introduction to Bases
So, WHAT IS BASE? All right. So when we count starting Zero we count zero, one, two, three, four, five, six, seven, eight, nine. Book comes after nine ten, right. But how do we write down ten? We write down the number one followed by the number zero. The one in this case is next to zero to its left. So it represents ten times what it would usually represent, which would be one resulting in ten times one or ten total the Zeros added to this for a total of ten. If we had eleven, we would add one to ten for a total of eleven because we'd have a one in a one in a row another example of deconstructing the. Number system can be applied to some random number. Say Seventy Nine, seventy nine is written as a seven next to a nine. The nine is all the way on the right and since the seven to the left of the nine, it is an the tens place. So seven times ten is seventy plus nine, seventy nine the system continues like that one, thousand, two, hundred, thirty, four means four, plus three times ten. Plus Two Times one hundred, which is ten times a privilege multiplier, which was ten plus one times. One, thousand, which ten times the previous multiplayer, which is one hundred. which so as the total is one, thousand plus two, hundred plus thirty plus four is one, thousand, two, hundred and thirty four as you go left, the place gets ten times bigger with every digit. This is what it means. When we say we use base ten place value system. There are ten digits zero through nine and we use them in a row to denote quantities and the cool part is that in. A very short space. You can count all sorts of things you can count, for example, the number of particles in the universe the number of particles in the universe can be written down using only eighty characters for reference. The sentence that you just heard contains a total of ninety five characters. One, hundred four if you include spaces and if every particle were planet with around ten billion people on it, you count all. Those people with only ten more characters. Ninety toto is a perfectly optimized system for denoting exact imagers and with the ratings pointed to be used for fractional number as well. But more than that. Later, these numerals zero through nine that is are known as the Hindu Arabic numerals our developed between the first and fourth centuries ce by Indian mathematicians, they're introduced to Europe between the tenth and sixteenth centuries he interesting. So. So, in other words to summarize that in say one or two sentences don't don't quote me on that. Essentially when we talk about a place value system and basis, we talk about what is the fewest amount of symbols rather what what, what are the total amount of symbols that are used to in any sort of combination represent any arbitrary number up through infinity well, I suppose infinity would be its own symbol really. Number approaching infinity as we're seeing earlier in in our number system, which is the Hindu Arabic number system We have just ten symbols zero through nine that's it, and we represent every conceivable number using those symbols. I should probably add to that also irrational numbers like pie or e an infinity and things like that. But a very small number of symbols can represent almost a really an infant number of possible symbols can be represented by this finite system. And what's interesting is as we talk about different bases, it's just a different number of symbols and the most fundamental one binary. It's either a one or zero or an hour and honoring anything else whether it's are based ten or hex decimal or anything like that. It's just an arbitrary number of symbols to work with which you using. Yeah. Exactly. Am Binary since we have either one or zero, we have two different bases. Different symbols. So we are in based to yes. Yeah. Binary base two, and if we had sixteen symbols, we'd be Anna Heck's the decimal. So. Real quick. I'd like to say a couple of definitions here based on what we just said about basis in about symbols, bring us to our discussion about numerals versus numbers just for clarification numerals are what you write down. There are only ten. Sorry. My son is bringing a toy saw on a table. So with numbers versus numerals there are only ten numerals that zero through nine. However, those ten numerals are us to make any amount. So that's the difference between numerals and numbers any base system. The numerals are how many different symbols are included in that base.