| MadSci Network: Computer Science |
Let's break your question down into two parts:
This first part explains Binary Numbers and Binary Arithmetic. If you'd like more detail, here is a webpage I put up on this: BINARY NUMBERS AND ARITHMETIC
For the second question, here is a webpage I put up, from a class I developed, that explains how the calculator uses logic circuits, called gates, to add numbers: http://www.geocities.com/CapeCanaveral/Hall/4284/logiccircuits/logiccircuits.html
It shows how a half adder is made from more basic gates, an AND gate and an EXCLUSIVE OR gate.
I have a page that moves up from there and shows how the half adder is used to make a microprocessor (basically, what is inside a calculator..although there are also other uses for a microprocessor): http://www.geocities.com/CapeCanaveral/Hall/4284/simplecomputer/simplecomputer.html
Here is a photograph of a microprocessor:
Here is a previous Mad Scientist answer that shows how some logic gates are made from MOS transistors (sorry that one of the images is missing): 909439032.Cs.
...and here is another Mad Scientist's previous answer that shows how a MOS transistor works: 859495932.Eg
Try the links in the MadSci Library for more information on Computer Science.