Workings of a basic calculator?

[bobleny]

Now, we use calculators on a day to day basis, but how do they work? Most of us know that a basic calculator has a basic IC to perform the algorithms. I had a few questions I was hoping you could answer about this.

Everything in electronics deals with logic. If a condition is true, perform this action, if this then that. I know that 2+2 is equal to 4. However, a calculator doesn't "know" this. Its function is to figure it out. I'm just wondering how it does this. I can't figure out why 2+2=4. I have no idea why 2+2=4, I just know it does, so I've been told... My 50 cent calculator can figure it out though.... So here where my main questions.

What is the logic of these circuits?
How does it differentiate between a 0, 1, 9, or an 3?
What is the logic circuit used to preform the mathematical computation of 2+2?

I would really like someone to break it down step by step and perhaps provide a basic diagram of the logic used. I don't need to know the components to build a calculator, I just want to see the gates a calculator would use to perform 2+2.

Edit: I think the diagram I am thinking of is called a block diagram....

 

[monoman]

a calculator is able to differentiate between denary numbers (1,2,3..) by storing them as binary numbers in digital memory (like ascii in programming). when you press say number 2 on the calculator, the calculator will recall the binary number 1 0 from its memory. all of the calculations done by the calculator are then done by logic gates that deal with the 1's and 0's that make up the binary numbers being inputted from the memory. at the end the answer to the sum is converted back from binary into a sequence of lines (stored in memory)on an LCD display making up the denary digits we want our answer to be displayed in.

>Subtraction, multiplication, and division functions on a calculator are all possible to impliment by using addition in different ways. 
>therefore addition is this basis of all these common functions
>the most simple circuit allowing you to add together two binary numbers is the HALF ADDER
>this is then extended to make a FULL ADDER
>full adders can then be joined together to allow us to add together larger and larger binary numbers
>they can also be combined in certain ways to be capable of subtraction, multiplication, and division

This is one of my favourite websites for basic digital electronics; this page shows you the half-adder and full-adder circuits with an explanation:

http://www.play-hookey.com/digital/adder.html

,monoman