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We've covered a lot of ground, shared a few laughs, and now I want to review where we are now and how we got here before we move on to the next topic.

First we talked about single bits, how they are "things" (whatever that means) that are always in one of two states (on/off, up/down, 0/1, black/white, whatever). Bytes are series of 8 bits, and can be used to represent binary numbers. Binary numbers use base two (instead of base ten in decimal), so all of their digits are either 0 or 1, and these digits can very conveniently be represented by individual bits.

Once we had some understanding of binary numbers we moved on to performing math on those numbers. First we talked about the single-bit adder, and then how we can perform multi-bit addition using a series of single-bit carry adders.

Next we talked about computer memory. Computer memory is like a big long ordered list of numbers. Each number in the list has an address associated with its place in the giant list, so if you know a memory address you can look to see what number lives there. Loading means to read a number from the memory and storing means to put a number into the memory (destroying forever what was in that memory location before).

We also talked about what kinds of information those numbers in the memory can represent. They can be either instructions or data. Data can have any meaning given to it by the person programming the computer. For example a programmer could interpret a binary number in the memory as a few things: the number itself, a specific color, a location on a map, a kind of food, or anything really. It just depends on what the programmer wants for the data to stand for. It's up to the programmer to be consistent with how he treats the data, because the computer itself doesn't care about that at all.

Instructions are the other kind of information that can be stored in memory. Instructions tell the computer's processor what to do next. There's a special register in the processor called the program counter (PC) that tells the processor where, in the memory, its next instruction will come for. The processor fetches (or loads, in memory terms) that instructions, figures out what it says to do, and then does it. After this it moves on tot he next instruction (by increasing the PC) and repeats the process.

Or does it? We also learned about special processor instructions called jumps and branches which directly change the value of the program counter. Jumps unconditionally change the value of the PC to whatever the programmer wants. Branches might change the value of the PC, depending on some condition, like if one variable's value is greater than another variable's value. Once we knew about branching and jumping we could write just about any computer program under the sun, and we looked at an example that shows how we can create a loop using branches and jumps that adds a number to itself several times, essentially performing multiplication.

The last thing we talked about is the register file of the processor. Each processor has a number of registers that are temporary storage for whatever's in the memory, and act as the variables in all of the instructions the processor can execute. The registers don't have addresses the say way that memory locations do, but they still do have distinct names, like $r0 and $r17. Long, complicated programs consist of many loads from memory into registers, additions, branches based on the contents of registers, jumps, and stores back into memory. Even the most complicated programs can be broken down into these elemental pieces.

The last thing we talked about is one other operation that we can perform on registers, and that is the shift. Shifting can be done in either the right or left direction, and these operations are mathematically similar to division and multiplication. The catch is that a single shift operation can only multiply or divide by powers of two. If you want to multiply by numbers other than powers of two, then you need to get more creative. We'll talk about these ways at some future time.

And now we're here. If you missed any posts go back and start from the beginning. I'm trying to build on all of my previous posts, hopefully forming over time one big picture of computer science that anyone can understand.