Read Online But How Do It Know? - the Basic Principles of Computers for Everyone by J Clark Scott - Free Book Online Page A
Authors: J Clark Scott
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The method for using these symbols is that you write down a “|” for each of the first four things you are counting, then for the fifth mark, you write a “/” across the first four. You repeat this over and over as long as necessary and then when you’re done you count the marks by groups of five – 5, 10, 15, 20, etc. This system is very good for counting things as they pass by, say your flock of sheep. As each animal walks by, you just scratch down one more mark – you don’t have to cross out ‘6’ and write ‘7’. This system has another advantage in that there is actually one mark for each thing that has been counted. Later in the chapter we are going to do some interesting things with numbers that may get confusing, so in order to keep things clear, we will make use of this old system.
Do you remember Roman numerals? It is a number system that also consists of two elements. The first element is the symbols, just selected letters from the alphabet, ‘I’ for one, ‘V’ for five, ‘X’ for ten, ‘L’ for fifty, ‘C’ for one hundred, ‘D’ for five hundred, ‘M’ for one thousand. The second element is a method that allows you to represent numbers that don’t have a single symbol. The Roman method says that you write down multiple symbols, the largest ones first, and add them up, except when a smaller symbol is to left of a larger one, then you subtract it. So ‘II’ is two (add one and one,) and ‘IV’ is four (subtract one from five.) One of the things that made this author very happy about the coming of the year 2000 was the fact that Roman numerals representing the year got a lot simpler. 1999 was ‘MCMXCIX,’ you have to do three subtractions in your head just to read that one. 2000 was simply ‘MM.’
The normal number system we use today also consists of two ideas, but these are two very different ideas that came to us through Arabia rather than Rome. The first of these ideas is also about symbols, in this case 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. These digits are symbols that represent a quantity. The second idea is a method that we are so used to, that we use it instinctively. This method says that if you write down one digit, it means what it says. If you write down two digits next to each other, the one on the right means what it says, but the one to its left means ten times what it says. If you write down three digits right next to each other, the one on the right means what it says, the middle one means ten times what it says and the one on the left means one hundred times what it says. When you want to express a number greater than 9, you do it by using multiple digits, and you use this method that says that the number of positions to the left of the first digit tells you how many times you multiply it by ten before you add them up. So, if you have ‘246’ apples, that means that you have two hundred apples plus forty apples plus six apples.
So how does this work? A number of any amount can be written with the digits zero through nine, but when you go higher than nine, you have to use two digits. When you go above ninety-nine, you have to use three digits. Above nine hundred ninety-nine, you go to four digits, etc. If you are counting upwards, the numbers in any one of the positions go ‘round and ‘round - zero to nine, then zero to nine again, on and on, and whenever you go from nine back to zero, you increase the digit to the left by 1. So you only have ten symbols, but you can use more than one of them as needed and their positions with regard to each other specify their full value.
There is something odd about this in that the system is based on ten, but there is no single symbol for ten. On the other hand, there is something right about this – the symbols ‘0’ through ‘9’ do make up ten different symbols. If we also had a single symbol for ten, there would actually be eleven different symbols. So whoever thought of this was pretty smart.
One of the new
Do you remember Roman numerals? It is a number system that also consists of two elements. The first element is the symbols, just selected letters from the alphabet, ‘I’ for one, ‘V’ for five, ‘X’ for ten, ‘L’ for fifty, ‘C’ for one hundred, ‘D’ for five hundred, ‘M’ for one thousand. The second element is a method that allows you to represent numbers that don’t have a single symbol. The Roman method says that you write down multiple symbols, the largest ones first, and add them up, except when a smaller symbol is to left of a larger one, then you subtract it. So ‘II’ is two (add one and one,) and ‘IV’ is four (subtract one from five.) One of the things that made this author very happy about the coming of the year 2000 was the fact that Roman numerals representing the year got a lot simpler. 1999 was ‘MCMXCIX,’ you have to do three subtractions in your head just to read that one. 2000 was simply ‘MM.’
The normal number system we use today also consists of two ideas, but these are two very different ideas that came to us through Arabia rather than Rome. The first of these ideas is also about symbols, in this case 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. These digits are symbols that represent a quantity. The second idea is a method that we are so used to, that we use it instinctively. This method says that if you write down one digit, it means what it says. If you write down two digits next to each other, the one on the right means what it says, but the one to its left means ten times what it says. If you write down three digits right next to each other, the one on the right means what it says, the middle one means ten times what it says and the one on the left means one hundred times what it says. When you want to express a number greater than 9, you do it by using multiple digits, and you use this method that says that the number of positions to the left of the first digit tells you how many times you multiply it by ten before you add them up. So, if you have ‘246’ apples, that means that you have two hundred apples plus forty apples plus six apples.
So how does this work? A number of any amount can be written with the digits zero through nine, but when you go higher than nine, you have to use two digits. When you go above ninety-nine, you have to use three digits. Above nine hundred ninety-nine, you go to four digits, etc. If you are counting upwards, the numbers in any one of the positions go ‘round and ‘round - zero to nine, then zero to nine again, on and on, and whenever you go from nine back to zero, you increase the digit to the left by 1. So you only have ten symbols, but you can use more than one of them as needed and their positions with regard to each other specify their full value.
There is something odd about this in that the system is based on ten, but there is no single symbol for ten. On the other hand, there is something right about this – the symbols ‘0’ through ‘9’ do make up ten different symbols. If we also had a single symbol for ten, there would actually be eleven different symbols. So whoever thought of this was pretty smart.
One of the new
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