CS THEORY: Memorable numbers

See, I told you this would be the title of the next article.

I've decided to start with something that is more fundamental to computer science, and less fundamental to computer architecture. I think talking about the concepts behind computer memory from a theoretical, mathematical kind of perspective will be more valuable to more people when starting out than talking about binary mathematics. So for now, I'm not going to talk about binary numbers (although you're welcome to imagine all the numbers I do talk about as such if you like). Instead, I'm going to talk about regular numbers and memory cells.

I kind of struggled with how I wanted to explain computer memory this time. Last time I talked about a lineup of bathtubs filled with binary digit buckets. That was pretty weird, in retrospect. Let's move away from that and talk instead about regular numbers and boxes that can hold those numbers.

Imagine a spreadsheet. Imagine the giant grid that extends on forever to the right and down, with the alphabet along the top naming each of the columns, and the numbers along the side naming the rows. Now, erase columns B-infinity, so we're left only with column A. This is a pretty good way to visualize computer memory. A single, numbered list of boxes that can each hold a number. It doesn't really make a difference whether you imagine this numbered list of boxes as being vertically or horizontally oriented, but for the sake of space efficiency, I'm going to write it out as a horizontal row of boxes of numbers. Here it is:

[_] [_] [_] [_]

Imagine that as 4 boxes, none of which currently has a number in it. I just got tired of typing those out after 4 boxes, but in real computer memory there are billions. Yeah, billions. That's a lot. One of the things about these memory boxes, or "memory cells" as I'm going to call them, is that they *need* to hold numbers. They can't actually be empty. So let's put some numbers in there:

[83] [101] [116] [104]

Pretty good numbers, right? Let's list some things we could do with those numbers. Well, we could add two of them together, we could multiply two of them together, we could do any kind of math on them that we want. Those are pretty predictable uses of numbers. One thing about computers, though, is that the computer doesn't care what we do with those numbers or what we pretend those numbers mean (unless we ask the computer to do math on those numbers, then the computer will treat them as numbers and do the math correctly).

In fact, those numbers I listed up above are not totally random. There is a way of pretending that numbers are actually letters and symbols called ASCII that says that those numbers I chose up there actually stand for something else. According to ASCII, the 83 stands for 'S', the 101 stands for 'e', the 116 stands for 't' and the 104 stands for 'h'. So [83] [101] [116] [104] can actually stand for "Seth" (that's my name, by the way).

Now to relate this to the computer you're reading this on right now. Your computer has billions of memory cells, each with some kind of number in it, and those numbers can mean things that humans can understand, like letters we can read, or colors we can see, or sounds. Since I typed out this word "Seth" and your computer downloaded this webpage so it could be displayed on your screen, somewhere in your computer's memory is the sequence of numbers: [83] [101] [116] [104].*

From today's article I hope you got an idea that there is a series of memory cells in your computer and each cell holds a number in it. These numbers can be meaningful to humans in ways other than just how we understand numbers as numbers. We used the example of the ASCII encoding for the word "Seth" as a way to understand how a series of numbers can really be understood as a series of letters we can read.

Next time we talk about CS THEORY we'll talk about how memory cells are organized.

*Ok, so this webpage was probably encoded with some other number-to-text system than ASCII, but you get the point.