Peices of Eight
People count stuff. That means when they have things around them they naturally
want to know how many of each kind or how many of everything. They start to
count either in their subconscious or on purpose to get an idea how many are or
they could use perhaps.
There are systems of counting by many societies. One society I know of counts in fives
and I'm sure that there are those that count in eights or sixes. But in english people count
in tens: zero one two three four five six seven eight nine one-zero(ten). After this one starts again like:
ten-one ten-two ten-three ten-four ten-five ten-six ten-seven ten-eight ten-nine two-zero or two-tens(twenty).
After this you start again using two-ten or twenty like this: twenty-one twenty-two... etc and on and one
Machine Numb Thumbs
Now computers count in twos. That means:zero one one-zero(ten), ten-one one-zero-zero(one hundred) and so on...
This is how you count in twos for ten counts:
0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010
1 is added to the numbers to get to the next number as usual in number counting, but here we are counting using a
base of 2. It is also called counting in base 2 and it may be written like this: N2
N designates the number so 1010 is better written as 10102.
We know that 10102=1010
Lets count in eights or lets count in base 8. Here we go:
0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30...
You can see here that there is no '8' in the base 8 system. the number '8' is written like '10'. So in base-8 eight is
is the ten there.
A number in a base such as 134 in base 8 can't have 8 or a number greater than 8 in among its digits. For instance
you can't have 23948 because both 8 and 9 are equal to or greater than 8.
Like Packing Things in a Package in Production
When adding in other bases certain things must be taken in account such as carries and borrows.
for instance:
45+35=125
This means that 4+3 in base five is 2 greater than 5(or 10).
Let us do another one:
58+78 = 148(12 in base ten. 12-8 = 4)
What if you wanted to add 4156+3446?. You will have to do it like the old ways of summing.
You could arrange them one on top the other.
5 + 4 = 9 (in base 10). But this is "6+3", which means 910=136 So you put down 3 and carry 1. On the next line you add 1 + 1 +4 which is 6 in base 10 an this is 10 in base 6 You put down 0 and carry 1 and the next add is 1+4+3 which is 8 in base 10 meaning 126
The answer of 4156+3446is then 12036.
When subtracting any borrows will result in increasing the current number by 10 in the current base.
For example 10 is borrowed from the 1 in the top number, and the 10 is actually 6 in base 6. When put with the 2 you have 126
What you do is instead of saying 12 you call it 6+2 =8 , then you do the minus 8-4 = 4. You will always get a number less than 6
or the base in the answer digits When multiplying in other bases, its the same as adding only when you multiply each dou you do so first in base 10.
then you transform each one to the required base and do any necesary carries.
For instance let us say you needed to do
For example 4(this is the last 4 in bottom number 344) times 2(this is the last 2 in the top number 412 ) will yeild 8. This is greater than 6 by 2 i.e 8-6 =2. Therefore 810 = 126.
you should put down 2 and carry 1. The next process will be to say 4(this is still the last 4 in bottom number 344 as you nee to first run through all the top digits with it then move to the next 4)
times 1 + 1. This is because you need to add the carry from the back as per normal multiply operation.
4156
+3446
Take One Out the Pack
4126
-3446
Like All that is All the Packages in Production
4126
x3446
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