Building Your Own Computer Part 3:

ADDERS

First off i am sorry this one was so late, ijust havnt had a chance to get on my computer for he past

few days.

Today we are going to ease the knoledge from the last part (the different logic gates) combined

with some good old binary to create our first useful circuit.

lam sure at least some of you dont know binary so i will give you guys a basic rundown. I am sure

you are aware that our counting system uses the numbers , that is once you get to 9 that

column resets to , and the next one along sets itself to 1 ( so 9 goes to 1 in the next column and

resets itself to o to get 10) this makes it a TEN BASE COUNTING SYSTEM because there are 10

numbers before the column resets.

Well binary is a two base counting

each column

system that IS, there are only two

wand seams next

resets. This means the only two

numbers used in binary are o and

1 rather than o to 9. So an average binary number looks like 1010101110 or 110100111 instaed of

1202934 or 21892.

Now this is all well and good but will get you know where it you dont know how to convert a

number from binary to decimal and vice versa. We will cover the former first.

Converting form Binary to decimal

Before we can convert a number from binary to decimal, we need a number to convert, and

before we chose a number ithink we should probably learn the meaning of a very commonly

used term in binary, the byte. You have probably heard the term byte before (in the form of

gigabytes or terrabytes on for example). But what is a byte? A byte is 8 bits, and a bit is

simply one of the columns in binary, so in our normal counting system we have hundreds tens

and units columns, in binary these are called bits, and a byte is 8 of these bits. So any binary

number that has 8 columns is a byte, for example 01101100 or 11110000 would be bytes, but

011 would not as it is only 3 bits long.

Now that we know what byte is, lets convert one. Lets start with the number 10110101. To

convert a number from binary to decimal we need to draw out a small table with 8 columns and 2

rows (don' t worry once you get used to it you will be bale to do this easily in your head, this is

just to understand whats going on) like so:

Then you need to till out the top row from RIGHT To LEFT with powers of two, so in the first column

we need to do 240

so 1, then in the next do PI so 2, then 242 so 4 ( it you dont undertand just double each one) like

WEBER

Now that we have done that we need to till in the number we are going to convert (10110101)

into the bottem row like so:

Now we do an easy peasy add operation, to do this we go along our binary number and it

that bit is a 1 then we include whatever number is at the top in our add, it it' s we don' t. So

it we go along this byte we need to include: 128, 32, 16, 4 and 1. If we do we get the sum

which equals 181. It' s that simple (just to let you know the max number a

byte can have is 255)

So thats how you convert from binary to decimal, but what about the other way round?

Converting from decimal to binary

Because we are only dealing with bytes for now it makes this a bit easier, we simply have

to minus each power of 2 from the number till we get o. To break that down it we

converted 181 back to binary, we need to start with 128 (the highest bit in a byte)

in this case it does as - 53 so the 128 bit must be 1. Then we do it again for the

next power of 2 which is 64, but equals less than o so that bit must be , then we

go to the 32 bit, equals 21 which is more than , so the 32 bit must be 1. If we do

this for all the bits we get 10110101, which is correct. So thats how we convert decimal

to binary.

Now we know how to convert a byte from binary to decimal and vice versa, in the

next part we will explore binary addition, and we will also, build a basic adder, also

known as the half adder, then in the final part we will combine all of this to make a

full adder. Thanks for reading, again sorry it was so late.

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