Jumps, loops and clock speed.

Step 1 of 7

A program with a loop

The chip’s ALU has no multiply. To work out $3 \times 4$⁠ you add 3 four times, and rather than write the same instructions four times, you write them once and go back to them: a loop. This is the program now in memory:

Address	Instruction	What it does
0	LDA 13	loads the total so far
1	LDB 14	loads the number to multiply
2	ADD	adds it to the total
3	STA 13	stores the total
4	LDA 15	loads the rounds left
5	LDB 12	loads 1
6	SUB	takes away one round
7	STA 15	stores what is left
8	JZ 10	if no rounds are left, jumps to 10
9	JMP 0	goes back to the start of the loop
10	HLT	stops

Cell 12 holds 1, cell 13 the total, which starts at zero, cell 14 the number to multiply, 3, and cell 15 the number of rounds, set by the Rounds Parameter.

A jump is an instruction that writes a new address into the program counter. Clock tick stands at 27, the fetch of JMP 0 at the end of the first round: the counter has already gone up to 10.

Step 2 of 7

A conditional jump

If the loop ended with only JMP 0, the program would go round for ever. The JZ 10 before it is a conditional jump: it jumps only when the zero flag is on, and otherwise does nothing, so the processor goes on to the next instruction. This is how a computer makes decisions: every “if” in a program comes down to a conditional jump.

Step 3 of 7

Multiplying by adding

One round is ten instructions, addresses 0 to 9, which is thirty ticks. Step Clock tick on in jumps of thirty, and watch cell 13 grow with each round.

Now the number to multiply is 6, Rounds is 4, the lid is closed, and the program has already halted.

Step 4 of 7

Counting instructions

How long a program runs depends not on how many instructions are written in it, but on how many the processor actually carries out. In a loop the same instructions run again every round.

Step 5 of 7

From ticks to seconds

A processor’s clock ticks at a steady rate, its frequency, measured in hertz: ticks a second. To find how long a program takes, count its ticks, $N$⁠, and divide by the frequency, $f$⁠:

$t = \frac{N}{f}$⁠

The chip’s Clock speed is set to 1000 Hz. The board does not draw the clock; the rate only sets how long each tick lasts.

Step 6 of 7

A faster clock

There are two ways to cut the time: carry out fewer ticks, or speed up the clock. Here the program is fixed, which leaves speeding up.

Step 7 of 7

Real processors

The clock of a laptop’s processor ticks three or four billion times a second, 3 GHz to 4 GHz. But the clock speed alone does not say how much work gets done: you also need to know how many ticks each instruction takes.