How Computers Add - A Logical Approach

We looked at Number Systems and counting (see It's a Binary World - How Computers Count) last time. As a quick refresher, we saw that computers are made up of many units of 0 and 1,

Mississauga, Canada (prHWY.com) September 15, 2012 - We looked at Number Systems and counting (see It's a Binary World - How Computers Count) last time. As a quick refresher, we saw that computers are made up of many units of 0 and 1, the binary system. 1 is the highest digit possible so numbers in the computer are stored as for example 1010 or 10 in decimal. We also saw that these binary numbers can be seen as octal (8) or hexadecimal (16) numbers - in this case 1010 becomes 15 octal, or A hex.


You probably realise that the 'standard' PC code is in 8 bit bytes taking the hex system a stage further. You may also know that processors, and Windows software that runs on them, have progressed from 8 bits to 16 bits to 32 bits to 64 bits. Basically this means the computer can work on 1,2, 4 or 8 bytes at once. Don't worry if this is all Gobbledegook, you don't need it to understand how computers add!


OK now to the Math - cringe time! It's a little more complicated than last time, but if you think logically, like a computer, realising they are really dumb, you will sail through it!


We take a break here to look at a bit of math you may not have heard of - Boolean Algebra. Once again it's really simple, but it shows you how a computer works, and why it is so pedantic!


Boolean Algebra is named after George Boole, an English Mathematician in the 19th Century. He devised the logic system used in digital computers more than a century before there was a computer to use it!


In Boolean Algebra, instead of + and - etc. we use AND and OR to form our logic steps.
For example:-


x OR y = z means if x or y is present, we get z.
However,
x AND y = z means that both x and y need to be present to get z.
We can also consider an XOR (eXclusive OR).
x XOR y=z means that x or y BUT NOT BOTH must be present to get z.


That's it! That's all the math you need to understand how a computer counts. Told you it was simple!



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