Binary Numbers For Dummies

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Binary (meaning 'two') is the ones and zeros that computers use.  The reason for this, is that there are only two states an electrical circuit can be in. Known as on and off or 1 and 0, 1 for on and 0 for off.

By grouping 1's and 0's together, a computer, or electrical circuit can create letters numbers and 'True' or 'False. Every bit of info in a computer has a binary code assigned to it and the computer knows these, for example, the letter 'A' converts to '01000001' in binary.

Converting Binary Numbers to Decimal Numbers

This is quite simple.

Converting Binary to Decimal works by using a place value system.

Let's take the Binary 10010011:

First we go from right to left (starting with one) and double it till we reach the end: -

1 0 0 1 0 0 1 1
(128) (64) (32) (16) (8) (4) (2) (1)

Now, if the value (in binary) is 1, then that is true, and the number assigned should be added to our total. If it is 0 then that is false and the number assigned should NOT be added to our total so from the above, we get: -

1 0 0 1 0 0 1 1
True False False True False False True True

+128 0 0 +16 0 0 +2 +1
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
these are all added together

Once the numbers have been added we get 10010011 = 147. So basically, all we do is add all the true numbers together.

Now, if you can fugure out how to do that in reverse, which is a pain in the ass to say the least, you can convert Decimal to Binary.
Let me give you a hand.

Again...if the numbers are clumped together just split them into groups of 8. Simple

Converting Decimal to Binary

First you need to figure out how many binary places you need to cover the decimal amount.

Lets take a number...say.....36

What we do, is wright this down to help us: -

1 1 1 1 1 1 1 1
(128) (64) (32) (16) (8) (4) (2) (1)

Then we say..hmm is it more than 128..no, so we dont put a 1 there. is it more than 64...no, so we dont put a 1 there..etc etc.

You will stop at 32 if you have figured this out, now you need you use your extraordinary math talents to figure out which combination of numbers out of 32, 16, 8, 4, 2 and 1 add up to 36.

If you are following, you should have chose 32 and 4, ok, now that we have the correct numbers, this is what we do: -

We just put a one above all of our chosen numbers and a zero above the others, so we should end up with: -

00100100

Which is:-

0 0 1 0 0 1 0 0
(128) (64) (32) (16) (8) (4) (2) (1)

32 + 4 =36.

And that, as they say, is that.