11.001001000011111101101010100010001000 Arithmazium
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Addition

Binary addition all boils down to one plus one is two: 

  1 + 1 = 10

Think of the nerdy T-shirt:

There are 10 kinds of people in the world – those who understand binary and those who don't.

Once we master 1 + 1, binary arithmetic has a pretty simple addition table. 

  +|  0   1
  -+-------
  0|  0   1
  1|  1  10

Example

Here is an application of our addition table. The cs indicate carries into that bit position. It works just like elementary school arithmetic. 

       cc
    01100100      100
  + 00001101     + 13
  ----------     ----
    01110001      113

Remeber the mantra, "six plus seven is three, carry the one"? In binary, we have, "one plus one is zero, carry the one".

We do a lot of carrying in binary addition. It's tedious when computing by hand, but electronic circuits handle it easily. When the sum of two bytes leads to a carry out of the leftmost bit, that bit is lost to the byte forever. Most computer processors will save it in a special Carry bit, in case the code running wants to check for it.

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