Unit 8: The Computer

A register that counts itself

A program is a list of steps, and something has to keep track of which step you are on. That something is the program counter.

It is a register wired into an adder that adds one — and then straight back into itself. Every tick it becomes one bigger than it was.

A loop, with a register in it to make it legal.

HDL

CHIP Counter {
    IN i3, i2, i1, i0, load, inc, reset;
    OUT o3, o2, o1, o0;
    PARTS:
    PC4(i3=i3, i2=i2, i1=i1, i0=i0, load=load, inc=inc, reset=reset,
        o3=o3, o2=o2, o1=o1, o0=o0);
}

USE Counter;
SET i3=0, i2=0, i1=0, i0=0, load=0, inc=1, reset=0;
SHOW;
CLOCK;
SHOW;
CLOCK;
SHOW;
CLOCK;
SHOW;

It prints

o3=0 o2=0 o1=0 o0=0
o3=0 o2=0 o1=0 o0=1
o3=0 o2=0 o1=1 o0=0
o3=0 o2=0 o1=1 o0=1

Every loop you have ever written

Counting up gets you through a program once. Jumping is what makes loops and choices possible: instead of "one bigger", the counter takes a number you hand it.

load=1 jumps to whatever is on the input wires. reset=1 goes back to 0. Three Muxes decide between the three, one after another.

HDL

CHIP Counter {
    IN i3, i2, i1, i0, load, inc, reset;
    OUT o3, o2, o1, o0;
    PARTS:
    PC4(i3=i3, i2=i2, i1=i1, i0=i0, load=load, inc=inc, reset=reset,
        o3=o3, o2=o2, o1=o1, o0=o0);
}

USE Counter;
SET i3=1, i2=0, i1=0, i0=1, load=0, inc=1, reset=0;
CLOCK;
CLOCK;
SHOW;
SET load=1;
CLOCK;
SHOW;
SET load=0, reset=1;
CLOCK;
SHOW;

It prints

o3=0 o2=0 o1=1 o0=0
o3=1 o2=0 o1=0 o0=1
o3=0 o2=0 o1=0 o0=0

That is if. That is while.

Everything a program can do about *where to go next* is one wire deciding whether the counter loads or counts.

if, while, for, calling a function and coming back — all of it, down here, is a Mux picking between "one bigger" and "this number instead".

The whole machine, in one sentence

A computer does the same four things forever:

1. The counter says which step we are on.
2. That step is fetched from memory.
3. The ALU works something out.
4. A register remembers the answer — and the counter moves on.

Then it does it again. Billions of times a second, and never anything else.

A tiny machine that really runs

Here all three parts are wired into one circle: a counter that counts, an adder, and a register keeping a running total of everything the counter has said.

Watch the totals: 0, then 1, then 3, then 6. It is adding up 1 + 2 + 3 as it goes — and the total is always one tick behind the counter, because both registers grab their values at the same instant.

HDL

CHIP Machine {
    IN go, reset;
    OUT o3, o2, o1, o0, acc3, acc2, acc1, acc0;
    PARTS:
    PC4(i3=0, i2=0, i1=0, i0=0, load=0, inc=go, reset=reset,
        o3=o3, o2=o2, o1=o1, o0=o0);
    Add4(a3=acc3, a2=acc2, a1=acc1, a0=acc0, b3=o3, b2=o2, b1=o1, b0=o0,
         s3=n3, s2=n2, s1=n1, s0=n0);
    Register4(i3=n3, i2=n2, i1=n1, i0=n0, load=go,
              o3=acc3, o2=acc2, o1=acc1, o0=acc0);
}

USE Machine;
SET go=1, reset=0;
CLOCK;
SHOW;
CLOCK;
SHOW;
CLOCK;
SHOW;
CLOCK;
SHOW;

It prints

o3=0 o2=0 o1=0 o0=1 acc3=0 acc2=0 acc1=0 acc0=0
o3=0 o2=0 o1=1 o0=0 acc3=0 acc2=0 acc1=0 acc0=1
o3=0 o2=0 o1=1 o0=1 acc3=0 acc2=0 acc1=1 acc0=1
o3=0 o2=1 o1=0 o0=0 acc3=0 acc2=1 acc1=1 acc0=0

You built a computer

Start to finish, everything you made came out of one gate that says "not both", plus a flip-flop that waits for the beat.

Not, And, Or, Xor. Choosing. Numbers. Adding. A calculator that does six jobs. Memory. A counter that can jump.

That is a computer. The one you are holding is the same, only wider and very much faster — and made of exactly this.