Score Reel
The click-click-click an old pinball table makes when you hit something good is not a sound effect. It is the arithmetic, happening at the speed of a motor, because the machine has no other way to count.
New to computer arithmetic? Start here
Numbers in a fixed-size box
A number on paper can be as long as it needs to be. A number in a computer gets a fixed number of digits and no more, so there is always a largest one it can hold and always a smallest difference it can tell apart.
Almost everything surprising about computer arithmetic follows from that. What happens when you count past the largest value depends on which kind of number it is: a fixed-width integer wraps round to the smallest, and a floating-point number goes to infinity instead. A value too fine for the gap is not rejected, it is rounded to the nearest one that fits, and then the rounding is added to the next rounding. These are not faults in the machines here. They are the edges of the box, and the machines are what people built to live inside it.
The machine for this idea on its own is Two's Complement, if you would rather press it than read about it.
The reels
Hit a target
1 Close: a target switch closes once, whatever the award is worth
2 Pulse: the score motor turns that one closure into as many pulses as the award
3 Count: each pulse steps a reel by one digit, at the motor's speed and no faster
4 Carry: a reel rolling through zero sends a pulse to the one on its left, and that one can send another
Every digit on those reels arrived as a pulse, and every award in this table ends in a zero because the units digit is painted on. That was a common arrangement and not a universal one: plenty of machines drove a real units reel and scored in ones.
Checked when this page loaded: of 6 awards, 0 needed a fraction of a pulse. Nine nines plus one pulse rolls to zero, carrying through all 5 reels. The units digit is fixed at 0, so the smallest thing this machine can score is 10.
A machine with no adder
There is no separate register in an electromechanical pinball table holding a number that the drums then display. There is no accumulator and no arithmetic unit. What there is, is stranger and better: the position of each drum is one decimal digit of the stored score, so the display is the memory. There are drums with digits printed on them, and a coil beside each drum that advances it one digit when it is energised. That is the entire vocabulary.
So a target worth fifty points cannot send fifty anywhere. It closes one switch, once, and something else has to turn that single closure into five separate energisings of the ten-point reel. That something is the score motor: a motor turning continuously with cams on its shaft, opening and closing stacks of switches as it goes round. Ask it for five pulses and it delivers five, at its own speed, and you wait.
Why the sound is the sum
This is why a big award on an old table takes time you can hear. Five thousand points is five pulses of the thousand reel, and the motor will not be hurried, so the machine counts out loud while the ball is still in play. On a good table you learn to hear what you scored before you look up.
It is also why every score you have ever seen on one of these ends in a zero. The units digit is usually not a reel at all: it is painted on the glass, because nothing on the playfield was ever worth less than ten and a drum that never moves is a drum you need not buy.
Carry is a piece of metal
When a reel goes past nine it trips a pawl, and that pawl advances the reel to its left. If that one was also on nine, it trips the next. A carry is a physical chain running left along the row, one reel at a time, and a long one is audible as a distinct rattle.
That is a ripple-carry adder built out of steel, and it has the same property the electronic kind has: the worst case is the whole width of the register. Five nines and one more pulse is five separate trips, and then the score is zero again, because there is no sixth reel for the carry to reach. Machines rolled over, and players kept count on their fingers.
These ran in this browser when the page loaded. Each claim, whether it held, and the number behind it.
| claim | held | measured |
|---|---|---|
| a 50-point target closes one switch and costs 5 pulses, reading 50 | yes | the score motor turns at its own speed, so this takes 750 ms and cannot be hurried; the audible time is the arithmetic happening |
| at 90, one more pulse carries into the next reel and reads 100 | yes | the tens reel returns to zero and its pawl trips the hundreds; nothing decided this, the drum simply came round |
| from 999990 one more pulse reads 0, and the machine has no way to know | yes | there is no register behind the reels, so what falls off the end is simply gone; this page counts it because it can, and the machine could not |
| one pulse scores 10 and not 1, because the units digit is painted on rather than turning | yes | five drums and a painted zero, which is why every award on the playfield ends in one |
| 5 awards totalling 1660 take 166 pulses and 24.9 seconds of clicking | yes | the count and the score are the same number in different units; there is nothing in this machine that adds |
What is real here, and what is not
There is no table
No ball, no flippers, no playfield, no physics of any kind. What a target is worth, and whether you could realistically hit it, is the design of a particular machine and is not modelled. This is the counting, which is the part that is arithmetic.
The clicking is synthesised, and it is not a recording
This page's whole argument is that the counting is audible, so it had better be audible, and it now is: one click per pulse, and a heavier one when a pawl reaches the next reel, because those are two different events on a real machine.
The pitch changes with the reel because a real table carried a chime unit: separate coils striking separate chimes, so ten points and a thousand arrive as different notes and a player knows which without looking up. Three chimes was the usual arrangement, so anything above the thousands here reuses the lowest rather than inventing a fourth that nobody had.
None of it was sampled. It used to be a filtered noise burst, and this ledger used to say that anyone who had stood next to a machine would know the difference immediately, which was true. It is now built from the three things that sentence named. The impact is the plunger arriving, three and a half milliseconds of broadband noise. The chime is a bar, because a chime unit is a solenoid throwing a plunger against a metal bar, and a bar free at both ends has transverse modes in a ratio that does not depend on its size or its tuning: 1, 2.76, 5.40, 8.93. Those ratios are inharmonic, and that is the whole reason struck metal sounds like struck metal. The cabinet is one low resonance under both. Measured after the change: each pulse rings for about 95 milliseconds instead of being cut off at 10, and its energy sits on the chime's own frequency and the cabinet's instead of smeared across an octave. The upper modes are real in the model and brief in the ear; do not expect to pick them out. It is still synthesis and still not a recording, and the cadence, 150 milliseconds between pulses, is the part that carries the arithmetic.
The motor speed here is plausible, not measured
The pulse rate on this page is a reasonable one for the era. It is not taken from a specific machine, and real cadences differed by manufacturer, by model and by year, as did the number of positions on the motor's cams. Treat the rhythm as indicative and the arithmetic as exact.
The relay logic is missing entirely
On a real table the score motor also sequences the game reset, the ball-in-play and player-up steppers, the bonus count-down and the match at the end, all through ladders of relays and stacks of switches. None of that is here. This page models one thing the motor does.
Five reels is a choice, and machines varied
Six-digit displays with a painted units zero were common in the era this page describes, and that is what is drawn. Earlier machines scored in far smaller numbers with fewer reels, and later ones went further. The rollover shown here belongs to the machine as drawn, not to every machine.
Sources
- US Patent 3,390,255, Roman F. Garbark, assigned to D. Gottlieb & Co., filed 1965 — “Stepping mechanism for use in a pinball machine or the like”, which is the reel this page models, described by the people who built it as “an improved counter mechanism of the drum type suitable for tallying the score in a coinoperated amusement device”. The manufacturers' own schematic manuals would be better still and are not available: Gottlieb enforces copyright on them and they were pulled from the pinball database. A patent is what is left that the maker wrote.
- Fun With Pinball, the score motor circuits animated
- Home Pinball Repair, on score reels
- PinWiki, electromechanical repair