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 Computer Architecture

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Tish
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PostSubject: Computer Architecture   Fri Oct 01, 2010 9:52 am

Anything on computer architecture place here or if anyone wants to know more information about it I will be placing it here.
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Tish
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PostSubject: Base 16   Tue Oct 05, 2010 1:32 pm

The Uniqueness of 16…

The first four odd numbers added – 1+3+5+7 equals 16.
A compass rose is divided into 16 points.
Chessboards have 16 black and 16 white pieces.
They are divided into four quadrants of 16 squares each.

Bookbinders use a standard format of sixteenmo, where the paper is divided into sixteen leaves.
Caterpillars usually have 16 legs! (But only 6 when they become butterflies).
Pre-decimal Imperial weights and measures used 16 ounces to a pound.

computers can only store and manipulate data in a binary base – base 2.

The earliest computer programs were written in binary by highly trained mathematicians. They were, however, highly prone to errors….

A method had to be found to “convert” large binary numbers to something that humans find easier to read and manipulate.

As base 2 does not convert to base 10 very easily, we use base 16 – hexadecimal – instead

Each Hexadecimal column uses a power of 16.



65536 4096 256 16 1

164 163 162 161 160

1 8 A 0 9 (these numbers are supposed to be spread out more like 1 under 164 and 8

under 163)


But we only have 10 unique symbols using the digits 0 to 9.
So to make up 16 symbols, we use the letters A – F as well.


The above number is worth 100873 in a decimal base.
We get this by multiplying and adding…..
(1x65536) + (8x4096) + (10x256) + (0x16) + 9




Last edited by Tish on Tue Oct 05, 2010 2:15 pm; edited 1 time in total
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Frodo
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PostSubject: Re: Computer Architecture   Tue Oct 05, 2010 1:47 pm

That is seriously cool. Very Happy
I'll have to show Ben, he is a maths geek.

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Tish
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PostSubject: Re: Computer Architecture   Tue Oct 05, 2010 2:22 pm

Mischievous, scandalous, utterly filthy and deliciously bad wrote:
That is seriously cool. Very Happy
I'll have to show Ben, he is a maths geek.

I have a lot more information too. This mainly helps with computer programming/ software courses. But in the engineering parts I will have information for calculus, dynamics and structures if you would like to take a look when its finished. Smile
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Frodo
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PostSubject: Re: Computer Architecture   Tue Oct 05, 2010 2:29 pm

Oh yes. Maths is cool. Very Happy

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Tish
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PostSubject: Converting to hexidecimal using 16 bit storage   Tue Oct 05, 2010 2:42 pm

Example – convert this number to hexadecimal using 16 bit storage

1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0

Always begin by dividing the binary number into “nybbles” (groups of 4) working from right to left

Each nybble can only hold a value of between 0 and 15.
Replace each nybble with the equivalent hexadecimal digit….

1001 1110 0011 1010

9 14 or E 3 10 or E

and 16 binary digits have been replaced with 4 hexadecimal ones!

expand each hexadecimal digit to four binary ones….

E 7 F 4 C 0 1 B

1110 0111 1111 0100 1100 0000 0001 1011

and your 8-digit hexadecimal number has become a 32-bit binary one!
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