How do arithmetic operators work in python?

Question

I am wondering how the "+" operator works in python, or indeed how any of the basic arithmetic operators work. My knowledge is very limited with regards to this topic, so I hope this isn't a repeat of a question already here.

More specifically, I would like to know how this code:

a = 5
b = 2
c = a + b
print (c)

produces the result of c = 7 when ran. How does the computer perform this operation? I found a thread on Reddit explaining how the computer performs the calculation in binary ( https://www.reddit.com/r/askscience/comments/1oqxfr/how_do_computers_do_math/ ) which I can understand. What I fail to comprehend however is how the computer knows how to convert the values of 5 and 2 into binary and then perform the calculation. Is there a set formula for doing this for all integers or base 10 numbers? Or is there something else happening at a deeper hardware level here?

Again I'm sorry if this a repeat or if the question seems completely silly, I just can't seem to understand how python can take any two numbers and then sum them, add them, divide them or multiply them. Cheers.

Answer 1

Cool question.

First of all, I do not think that you can type a + b = c . It would rather be c = a + b .

When the computer calculates this, it first converts 2 and 5 into binary. So 2 gives 10, and 5 gives 101.

The two binary numbers are added in the same way that any two base ten numbers are added, resulting in 111, which is then converted back to base ten as 7.

Answer 2

The numbers are always in binary. The computer just isn't capable of keeping then in a different numerical system (well, there are ternary computers but these are a rare exception). The decimal system is just used for a "human representation", so that it is easier to read, but all the symbols (including the symbol "5" in the file, it's just a character) are mapped to numbers through some encoding (eg ASCII). These numbers are, of course in binary, just the computer knows (through the specification of the encoding) that if there is a 1000001 in a context of some string of characters, it has to display the symbol a (in the case of ASCII). That's it, the computer don't know the number 58, for it, these are just two symbols and are kept in the memory as ones and zeros.

Now, memory. This is where it's getting interesting. All the instructions and the data are kept in one place as a large buffer of ones and zeros. These are passed to the CPU which (using its instruction set) knows what the first chunk of ones and zeros (this is what we call a "word") means. The first word is an instruction, then the argument(s) follow. Depending on the instruction different things happen. Ok, what happens if the instruction means "add these two numbers" and store the result here?

Well, now it's a hardware job. Adding binary numbers isn't that complicated, it's explained in the link you provided. But how the CPU knows that this is the algorithm and how to execute it? Well, it uses a bunch of "full-adders". What is a "full-adder"? This is a hardware circuit that by given two inputs (each one of them is one bit, ie either one or zero) "adds" them and outputs the result to two other bits (one of which it uses for carry). But how the full-adder works? Well, it is constructed (physically) by half-adders, which are constructed by standard and and xor gates. If you're familiar with similar operators ( & and ^ in Python) you probably know how they work. These gates are designed to work as expected using the physical properties of the elements (the most important of them being silicon) used in the electronic components. And I think this is where I'll stop.