A Simple Computer

Believe it or not, there is a huge advantage in studying a very simple computer before diving into the not-very-simple i7.

Basic Components

This is going to be really simple. Our computer will have:


At each “step”, the computer reads the memory word whose address is in $IP$ and then increments $IP$. Then it carries out the instruction that that word represents.

This is how most computers, uh, cores, work. It is called the fetch-execute cycle.

In this class, we’re not too concerned with how steps are synchronized; we’ll just say there’s a clock.

The Instructions

Each word that the computer tries to execute will be interpreted to have:

For a given instruction word, let’s call $op$ the first four bits, and $x$ the last 28 bits. We formally specify the operation of each instruction as follows. All arithmetic is signed, modular, 32-bit integer arithmetic.

0$A := M[x]$Load accumulator from memory
1$M[x] := A$Store accumulator to memory
2$A := P[x]$Read from a port into the accumulator
3$P[x] := A$Write accumulator out to a port
4$A := A + M[x]$Add into accumulator
5$A := A - M[x]$Subtract from accumulator
6$A := A \times M[x]$Multiply into accumulator
7$A := A \div M[x]$Divide accumulator
8$A := A \:\texttt{mod}\: M[x]$Modulo
9$A := A \wedge M[x]$Bitwise AND
A$A := A \vee M[x]$Bitwise OR
B$A := A \oplus M[x]$Bitwise XOR
C$IP := x$Jump to new address
Dif $A = 0$ then $IP := x$Jump if accumulator is zero
Eif $A < 0$ then $IP := x$Jump if accumulator is less than zero
Fif $A > 0$ then $IP := x$Jump if accumulator is greater than zero

An Example Program

This program, when loaded into memory at address 0, outputs powers of two, starting with 1, and going just past 1,000,000, to port 100 (64 hex):

Exercise: Write a program for this computer to generate the first 10 fibonacci numbers to port 7.
Exercise: Write a program for this computer to output Hello, world to port 888, assuming a UTF-32 encoding.
Exercise: Write, in the language of your choice, an interpreter for this computer. You will have to make a number of decisions regarding the user interface. Be creative.

Assembly Language

The example above was hard to read. Just listing the contents of memory that the processor executes is called “writing machine language.” Let’s use mnemonics for each instruction. Then the example becomes:

        JUMP    start    ; begin by jumping over the data area
pow:    1                ; store the current power value here
limit:  1000000          ; we'll be computing powers up to this amount
start:  LOAD    pow      ; bring the value into accumulator to use
        OUT     100      ; output the current power
        ADD     pow      ; adding to itself makes the next power!
        STORE   pow      ; store it (for next time)
        SUB     limit    ; we need to compare with limit, subtracting helps
        JLZ     start    ; if not yet past limit, keep going
end:    JUMP    end      ; this "stops" the program!

In general, each line of an assembly language program contains:

In our machine, the mnemonics will be: LOAD, STORE, IN, OUT, ADD, SUB, MUL, DIV, MOD, AND, OR, XOR, JUMP, JZ, JLZ, JGZ.

The process of converting from assembly language to machine language is called assembly. The reverse process is called disassembly. Yes, there exist programs called assemblers and disassemblers.

Exercise: Write an assembler for this computer. Consider writing it in JavaScript as a browser-based app, so that as you type assembly language in one window you immediately see the machine language in another.
Exercise: Suppose you were disassembling the word 100038A0. Is this an instruction to store the accumulator into memory address 0x00038A0, or is it a representation of the value 268449952? Or is it both? Why is this question philosophically interesting? Discuss.

What We Did Not Cover

The purpose of this simple computer is to introduce the basic concepts of the fetch-execute cycle and the difference between machine and assembly language. Things we haven’t covered include:

Moving On

If you found this machine interesting, here are things you can do: