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Full Version: How Computers Add - A Logical Approach
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You almost certainly realise that the...

We viewed Number Systems and counting (see It is really a Binary World - How Computers Count) last time. As a fast refresher, we found that computers are made up of several units of 0 and 1, the binary system. 1 is the highest digit possible so figures in the computer are located for example 1010 or 10 in decimal. We also found why these binary numbers is seen as octal (8) or hexadecimal (16) numbers - in cases like this 1010 becomes 15 octal, or A hex.

You almost certainly realise that the 'standard' PC signal is in 8 bit bytes using the hex system a stage further. It's also possible to know that processors, and Windows application that works to them, have progressed from 8 bits to 16 bits to 32 bits to 64 bits. Fundamentally what this means is the computer can perhaps work on 1,2, 4 or 8 bytes at once. If this is all Gobbledegook do not worry, you do not need it to comprehend how computers increase!

OK now to the [e xn y] - flinch time! It is a bit more difficult than last time, but you'll travel through it, if you think logically, such as a computer, realizing they're really foolish!

We simply take some slack here to look at a bit of z/n you might not have been aware of - Boolean Algebra. Once again it is really easy, but it demonstrates to you what sort of computer works, and why it is so pedantic!

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

In Boolean Algebra, instead of + and - an such like. we use OR and AND to form our logic methods.

For example:-

x OR y = z suggests if x or y is present, we get z.

But,

Y = z AND x means that both x and y need to be show get z.

We could also consider an XOR (distinctive OR).

x XOR y=z implies that x or y ALTHOUGH NOT BOTH must be show get z.

That is it! That's all the math you need to understand what sort of computer counts. Told you it absolutely was simple!

How do we utilize this reason in the computer? We make up a little electronic signal called a with transistors and things, so we could work on our binary quantities stored in a register - just a bit of memory. (And that is the final technology you'll hear about!). We make an gate, an gate, and an XOR gate

When we add decimal, as an example 9+3 we get 2 'models' and hold someone to the 10s, offering 10+2=12

Remember the binary bit values in Decimal 1,2,4,8 and so forth? We begin at 0 then 1 in the initial bit placement, the 1 bit. If we add 1 + 1 binary we have to finish up with 10, which has a 1 bit in the 2nd bit placement, and a 0 in the first, giving Decimal 2+0=2. This second bit position is formed by a CARRY from the very first bit.

To create an adder we must copy with a logic circuit the way we add in binary. To add 1+1 inputs are needed 3 by us, one for each bit, and a in, and 2 outputs, one for the end result (1 or 0), and a out, (1 or 0). In this instance the carry input isn't used. We use 2 XOR gates, 2 AND gates and an OR gate to create up the adder for 1 bit. I learned about rockwell trading by browsing the New York Guardian.

Now since now we have a Block, we go still another step, and just forget about gates, an ADDER. Our computer was created by utilizing various combinations of logic blocks. As well as the adder we might have a multiplier (a series of adders) and other parts.

Our ADDER stop takes one bit (0 or 1) from each number to be added, plus the Carry bit (0 or 1) and generates an output of 0 or 1, and a of 0 or 1. A dining table of the input A, T and Carry, and output O and Carry, appears like this:-

With no Carry in:

A B c O C

0 0 0 0 0

1 0 0 1 0

0 1 0 1 0

1 1 0 0 1

With Carry in:

A T c O C

0 0 1 1 0

1 0 1 0 1

0 1 1 0 1

1 1 1 1 1

This is known as a Table, it shows output state for almost any given input state.

Let us add 2+3 decimal. That is 010 plus 011 binary. ADDER blocks will be needed 3 by us for decimal bit values of 4) and 1, 2

The very first ADDER requires the Least Significant Bit (decimal bit value 1) from each number. Input A will be 0, input B will be 1 without any hold - 0.

From the truth table this gives a result of just one and a of 0 (3rd row). BIT 1 RESULT = 1

At once the following ADDER (decimal bit price 2) has inputs of 1, 1 and a of 0, providing a result of 0 with a bit of 1 (4th line). TOUCH 2 RESULT = 0

The following ADDER (decimal touch price 4) has inputs of 0, 0 and a of 1, giving a result of 1 without carry - 0 (5th row). BIT 4 RESULT = 1.

So we have bits 4,2,1 as 101 or 4+1=5.

It seems like a laborious solution to do it, but our computer may have 64 adders or more, adding simultaneously two vast quantities vast amounts of times another. Where in actuality the computer scores that is.

Next time we will get to how a computer performs more complcated procedures, and it is easy!.
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