# Binary Code - Addition

### When the number of bits available are limited

## An introduction to Binary

Binary Code is a mathematical code made out of zeros and ones. NO OTHER NUMBERS ARE USED. There is a Binary scale which starts at one and finishes at 128. { 1 2 4 8 16 32 64 128 } The zeros and ones make other numbers out of the numbers of the binary scale. Binary was called Base 2 which in other words means the number on the binary scale is multiplied by 2 each time until it gets to 128. But computers are backward so when you write it down you start at 128 and then finish at 1. WRITE RIGHT TO LEFT!

## Converting Binary to Denery (decimal)

Denery is really simple in other words Denery is our English numerical scale. Converting Binary to Denery is really simple. Firstly you have the binary you have to convert. For example, 00000011. What you do is you draw the binary scale, ( the binary scale is in the introduction ). Zero means cross out, in other words this number means nothing. One means keep the number so for instance. You have 128 64 32 16 8 4 2 1. Then with 00000011 you cross out everything apart from the 2 and the 1. Then you add the numbers remaining and there you have it. Your Denery number.

## The hard stuff. ADDITION.

Addition in binary is hard, but it's sounds simple. For example we all know that 1+0 = 1 and we all know that 0+0=0 but in binary 1+1=10. Crazy stuff right?! So when you have two binary nibbles for example 0101 and 1010 this will equal = 1111 because you do compact addition I.e the two sums are on top of each other:

__0101__

1010

Things get more complicated when you have to add two ones together with another one for example:

__1011__

0010 This Answer equals 1101. So you carry the one from the ten you get from the 1+1 and do what you would normally do in Maths and move it onto the next column. So you have 1+0=1 then 1+1=10 so you keep the 0 and carry the 1 so then you have 1+0 NOT 0+0 and then to finish 1+0 which equals 1 so your final answer is....... 1101 ........