24 Sep
2004
24 Sep
'04
9:39 a.m.
At 22:50 23/09/2004, you wrote:
On Wed, 2004-09-22 at 11:17 -0700, Vintage Computer
Festival wrote:
I did some back-of-a-fag-packet calculations (i.e. they might be completely
& utterly wrong, in which case I'd appreciate corrections) on a relay
computer...
Assume you want a Z80-type CPU. This has ~8k gates. Typically, it seems to
take 1 relay per input to implement any given gate. Now, I don't know how
many "x-input" gates there are in a Z80, so I'll assume that - on average -
it will require 3 relays/gate. Thus, we need ~24,000 relays to implement
the Z80.
If each relay needs, say, 25mA @ 6v to operate, then the peak current draw
of our R80 (as I shall call it) could be around 600A (I think). And that's
before we've added memory, i/o, etc.
As for the heat/noise - well, IMHO it's worth building it just to
experience that! Mind you, you'll need a lot of room: If you use 30mm by
13mm relays, then the board space you need is at least 9.36 square
metres... Still, if you assume that each board needs approx 40mm of space
incl. airflow room, then you should be able to fit the R80 into 2 400mm by
400mm by 2000mm cabinets (internal w/d/h)...
The relays I've been looking at typically quote around 25ms to operate
(either way), so I don't see how you could clock the R80 at anything faster
than around 40Hz; and you'd probably want to drop to 20Hz to be on the safe
side. The same relays quote a typical lifetime of 10e7 operations; so at
20Hz, your R80 should last a little under 139 continuous hours of operation
before relays started failing...
Creating a screen driver should be interesting....
Question: Wouldn't it be easier to implement an OR gate with no relays at
all (just two wires joining together)? Or would you need to use the relays
to keep the output voltage/amperage regulated?
Additional: Hunting around for a suitable CPU to implement in relays, I
came across the P8 CPU design (http://www.rexfisher.com/P8/P8_TOC.htm).
This uses a 74LS181 4-bit ALU, which I reckon would require 149 relays to
replicate. The only thing that confuzzles me is: what use, exactly, is a
1-input AND? Several of these appear on the 74LS181 schematic...
Cheers,
Ade.
On Wed, 22 Sep 2004, Jules Richardson wrote:
Amazing, huh? If I read that right, it's 52 relays though (I don't know
any German) which makes it sound rather like a 'simple' relay control
system rather than an actual relay computer. I fired off an email to
them to see if they'll let me have a nose at the wiring diagrams. Apologies if someone's mentioned this one
before. Quite possibly the
coolest gadget I've seen in a long time, though:
http://www.cyberniklas.de/pongmechanik/indexen.html
Awesome. It would be great to get stuff like this exhibited at the VCF.
The web page is pretty smart also. What terrific technical and design
work. 
24 Sep
24 Sep
10:03 a.m.
>>>> "Ade" == Ade Vickers
<avickers(a)solutionengineers.com> writes:
Ade> At 22:50 23/09/2004, you wrote:
> On Wed, 2004-09-22 at 11:17 -0700, Vintage
Computer Festival
> wrote: > On Wed, 22 Sep 2004, Jules Richardson wrote:
> >
> > > Apologies if someone's mentioned this one before. Quite
> possibly the > > coolest gadget I've seen in a long time, though:
> > >
> > > http://www.cyberniklas.de/pongmechanik/indexen.html
> >
> > Awesome. It would be great to get stuff like this exhibited at
> the VCF.
> >
> > The web page is pretty smart also. What terrific technical and
> design > work.
>
> Amazing, huh? If I read that right, it's 52 relays though (I don't
> know any German) which makes it sound rather like a 'simple' relay
> control system rather than an actual relay computer. I fired off
> an email to them to see if they'll let me have a nose at the
> wiring diagrams.
Ade> I did some back-of-a-fag-packet calculations (i.e. they might be
Ade> completely & utterly wrong, in which case I'd appreciate
Ade> corrections) on a relay computer...
Ade> Assume you want a Z80-type CPU. This has ~8k gates. Typically,
Ade> it seems to take 1 relay per input to implement any given
Ade> gate. Now, I don't know how many "x-input" gates there are in a
Ade> Z80, so I'll assume that - on average - it will require 3
Ade> relays/gate. Thus, we need ~24,000 relays to implement the Z80.
I think when people talk about "gates" in a logic design, it's
normalized back to the simplest kind: 2 input gates. So that's two
relays.
Meanwhile, remember that the original Pong didn't use a
microcomputer. It's just a board full of 7400 series ICs. It's been
too long since I saw one, but it doesn't seem unreasonable to do the
equivalent with 50 relays. For one thing, you don't need a video
generator, just motor controllers for the paddles and ball. And the
sending of ball hitting paddle or wall is done with contacts in the
mechanism, not with the logic itself. So the relay control has to
control motor speed and direction, but it doesn't have to track
position.
paul
2:17 p.m.
On Fri, 24 Sep 2004, Paul Koning wrote:
sending of ball hitting paddle or wall is done with
contacts in the
mechanism, not with the logic itself. So the relay control has to
Perhaps I read it wrong but the PONGMECHANIK uses logic to determine when
the ball has hit a paddle or wall.
"Element 2: The movements of ball and racquet, as well as the collision
detection take place in a metal chassis under the glass cover. Each moving
game compoent has a mechanical counterpart, which is moved by electric
motors. When these parts collide, contacts are closed and the relays in
the computer switch the direction of rotation of the motors."
--
Sellam Ismail Vintage Computer Festival
------------------------------------------------------------------------------
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2:55 p.m.
On Fri, 24 Sep 2004, Vintage Computer Festival wrote:
On Fri, 24 Sep 2004, Paul Koning wrote:
Hmm, upon further ponderance it seems like there is a combination of
mechanical contact and logic.
--
Sellam Ismail Vintage Computer Festival
------------------------------------------------------------------------------
International Man of Intrigue and Danger http://www.vintage.org
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sending of ball hitting paddle or wall is done
with contacts in the
mechanism, not with the logic itself. So the relay control has to
Perhaps I read it wrong but the PONGMECHANIK uses logic to determine when
the ball has hit a paddle or wall.
"Element 2: The movements of ball and racquet, as well as the collision
detection take place in a metal chassis under the glass cover. Each moving
game compoent has a mechanical counterpart, which is moved by electric
motors. When these parts collide, contacts are closed and the relays in
the computer switch the direction of rotation of the motors."
3:27 p.m.
>>>> "Vintage" == Vintage
Computer Festival <vcf(a)siconic.com> writes:
Vintage> On Fri, 24 Sep 2004, Paul Koning wrote:
> sending of ball hitting paddle or wall is done
with contacts in
> the mechanism, not with the logic itself. So the relay control
> has to
Vintage> Perhaps I read it wrong but the PONGMECHANIK uses logic to
Vintage> determine when the ball has hit a paddle or wall.
Vintage> "Element 2: The movements of ball and racquet, as well as
Vintage> the collision detection take place in a metal chassis under
Vintage> the glass cover. Each moving game compoent has a mechanical
Vintage> counterpart, which is moved by electric motors. When these
Vintage> parts collide, contacts are closed and the relays in the
Vintage> computer switch the direction of rotation of the motors."
What I meant is that the relay control is not doing position
calculation. It doesn't know where the ball and paddles are (only
whether certain motors are turning). Detecting ball hitting paddle
is by a contact on the ball carriage hitting a contact on the paddle
carriage.
In a sense the system is a hybrid computer: a digital control system
driving an analog computer. The analog computer is the set of motors
and switches on the playing field display. Or to put it differently:
the digital computer sets the motor speeds, and the analog computer
integrates that over time (double integral, dx and dy) to find the
position of the ball.
paul
3:55 p.m.
On Fri, 2004-09-24 at 16:27 -0400, Paul Koning wrote:
I was going to say that it does need to know what quadrant of the field
the ball is in so that it can return the ball to the centre position
after a point has been scored - but looking at the wiring diagram it's
actually cleverer than that (I'm having to learn German as I go, here).
All it does to return the ball is reverse polarity to the ball X/Y drive
motors when the ball goes out of play, and only stop each motor when it
reaches its respective centre line. Neat.
cheers,
Jules
>>>> "Vintage" == Vintage Computer Festival <vcf(a)siconic.com>
writes:
Vintage> "Element 2: The movements of ball and racquet, as well
as
Vintage> the collision detection take place in a metal chassis under
Vintage> the glass cover. Each moving game compoent has a mechanical
Vintage> counterpart, which is moved by electric motors. When these
Vintage> parts collide, contacts are closed and the relays in the
Vintage> computer switch the direction of rotation of the motors."
What I meant is that the relay control is not doing position
calculation. It doesn't know where the ball and paddles are (only
whether certain motors are turning). 
3:05 p.m.
Jules wrote:
I was going to say that it does need to know what quadrant of the field
the ball is in so that it can return the ball to the centre position
after a point has been scored - but looking at the wiring diagram it's
actually cleverer than that (I'm having to learn German as I go, here).
All it does to return the ball is reverse polarity to the ball X/Y drive
motors when the ball goes out of play, and only stop each motor when it
reaches its respective centre line. Neat.
Snap! I remembered!
In early 80's, there WAS a 5" x 9" x bit over 1" thick black toy.
Powered by battery, totally mechanical motor runnning all the time,
one dim red LED as "ball". Paddles slides side to side on each end.
To play, Turn on red dot glows (LED) press start button and motor
starts whirring audiably, the dot moves in fixed directions if it
bounces off the paddles, LED mechanically stiffly "rebounds" and goes
in different direction so on. A miss, the motor stops LED "ball"
still glowing. I did recall clearly that LED never ever rebounded
off the "side wall".
There was another similar mechanical flat toy but you "steer" the
race car around the objects on the invisible "belt" and miss them toy
keep going. Fun stops with flashing LED where racecar "exploded"
when racecar "bashed" something.
Cheers,
Wizard
10:37 p.m.
On Fri, 24 Sep 2004 jpero(a)sympatico.ca wrote:
In early 80's, there WAS a 5" x 9" x bit
over 1" thick black toy.
Powered by battery, totally mechanical motor runnning all the time,
one dim red LED as "ball". Paddles slides side to side on each end.
To play, Turn on red dot glows (LED) press start button and motor
starts whirring audiably, the dot moves in fixed directions if it
bounces off the paddles, LED mechanically stiffly "rebounds" and goes
in different direction so on. A miss, the motor stops LED "ball"
still glowing. I did recall clearly that LED never ever rebounded
off the "side wall".
That was the game "Blip!" by Tomy. I've got one (they're not that hard
to
find).
http://users2.ev1.net/~rik1138/Tomy/Blip.htm
There was another similar mechanical flat toy but you
"steer" the
race car around the objects on the invisible "belt" and miss them toy
keep going. Fun stops with flashing LED where racecar "exploded"
when racecar "bashed" something.
Mattel Auto Race
http://users2.ev1.net/~rik1138/Mattel/AutoRace.htm
The first hand-held electronic game (source: Evan Koblentz ;)
--
Sellam Ismail Vintage Computer Festival
------------------------------------------------------------------------------
International Man of Intrigue and Danger http://www.vintage.org
[ Old computing resources for business || Buy/Sell/Trade Vintage Computers ]
[ and academia at www.VintageTech.com || at http://marketplace.vintage.org ]
7:47 p.m.
On Fri, 24 Sep 2004 jpero(a)sympatico.ca wrote:
> In early 80's, there WAS a 5" x 9" x bit over 1" thick black toy.
Snip
in different
direction so on. A miss, the motor stops LED "ball"
still glowing. I did recall clearly that LED never ever rebounded
off the "side wall".
That was the game "Blip!" by Tomy. I've got one (they're not that hard
to
find).
http://users2.ev1.net/~rik1138/Tomy/Blip.htm There was
another similar mechanical flat toy but you "steer" the
race car around the objects on the invisible "belt" and miss them toy
keep going. Fun stops with flashing LED where racecar "exploded"
when racecar "bashed" something.
Mattel Auto Race
http://users2.ev1.net/~rik1138/Mattel/AutoRace.htm 
25 Sep
25 Sep
12:13 a.m.
New subject: Whats a HP1000M?
I noticed 14 of these coming up on govt Auction
http://cgi.govliquidation.com/auction/view?id=450006&convertTo=USD
I'd be interested but they are on the East coast...
10:22 p.m.
New subject: Whats a HP1000M?
I've been looking for some M series for a long time. I need just one, but
would take two. Anyone want to go in with me on a bid for them and take the
rest?
Jay West
----- Original Message -----
From: "Peter C. Wallace" <pcw(a)mesanet.com>
To: "General Discussion: On-Topic and Off-Topic Posts"
<cctalk(a)classiccmp.org>
Sent: Saturday, September 25, 2004 12:13 AM
Subject: Whats a HP1000M?
I noticed 14 of these coming up on govt Auction
http://cgi.govliquidation.com/auction/view?id=450006&convertTo=USD
I'd be interested but they are on the East coast...
26 Sep
26 Sep
12:47 a.m.
New subject: Whats a HP1000M?
put me down for a couple also.....
Thanks Ed Sharpe archivist for SMECC
Please check our web site at
http://www.smecc.org
to see other engineering fields, communications and computation stuff we
buy, and by all means when in Arizona drop in and see us.
address:
coury house / smecc
5802 w palmaire ave
glendale az 85301
----- Original Message -----
From: "Jay West" <jwest(a)classiccmp.org>
To: "General Discussion: On-Topic and Off-Topic Posts"
<cctalk(a)classiccmp.org>
Sent: Saturday, September 25, 2004 8:22 PM
Subject: Re: Whats a HP1000M?
I've been looking for some M series for a long
time. I need just one, but
would take two. Anyone want to go in with me on a bid for them and take
the rest?
Jay West
----- Original Message -----
From: "Peter C. Wallace" <pcw(a)mesanet.com>
To: "General Discussion: On-Topic and Off-Topic Posts"
<cctalk(a)classiccmp.org>
Sent: Saturday, September 25, 2004 12:13 AM
Subject: Whats a HP1000M?
I noticed 14 of these coming up on govt Auction
http://cgi.govliquidation.com/auction/view?id=450006&convertTo=USD
I'd be interested but they are on the East coast...
24 Sep
24 Sep
3:01 p.m.
On Fri, 2004-09-24 at 08:03, Paul Koning wrote:
I think when people talk about "gates" in a
logic design, it's
normalized back to the simplest kind: 2 input gates. So that's two
relays.
Well, with multi-terminal devices like relays, you get lots of outputs,
double-pole sort of "open collector". Plus, when circumstances allow it,
you can use ONE relay coil as two inputs; the two ends of the coil
winding are coil1 and coil2:
coil1 coil2
-v -v off
-v +v on
+v -v on
+v +v off
Can't do that with a transistor!
3:19 p.m.
On Fri, 2004-09-24 at 13:01, Tom Jennings wrote:
Plus, when circumstances allow it,
you can use ONE relay coil as two inputs;
...
Can't do that with a transistor!
Sorry, of course you can, but it takes extra components, and the point
with a relay is it is symmetrical (often or usually).
7:06 p.m.
double-pole sort of "open collector". Plus,
when circumstances allow it,
you can use ONE relay coil as two inputs; the two ends of the coil
winding are coil1 and coil2:
coil1 coil2
-v -v off
-v +v on
+v -v on
+v +v off
There were/are also relays with 2 coils. The idea is that either coil
alone will activate the contacts, but if you energise them both together
(in opposite directions), the magnetic fields cancel out, and the
contacts don't operate.
And of course there are magnetically-latched relays (effectively SR
flip-flops).
-tony
25 Sep
25 Sep
6:09 a.m.
Tony Duell wrote:
There were/are also relays with 2 coils. The idea is that either coil
alone will activate the contacts, but if you energise them both together
(in opposite directions), the magnetic fields cancel out, and the
contacts don't operate.
And of course there are magnetically-latched relays (effectively SR
flip-flops).
-tony
And slugged relays, with a big metal ring in the coil. These either
delay opening or closing, but I can't remember which way round it works.
I've got a few from old telephone exchanges - when I was about 12 or
13 I convinced my Dad to take a pickup truck full of BT phone exchange
"modules" from the local scrapyard.
Gordon.
6:04 p.m.
And slugged relays, with a big metal ring in the coil. These either
delay opening or closing, but I can't remember which way round it works.
I believe (without running upstairs to look in 'Telephony' [1]) that you
can arrange for either a slow make or a slow release
[1] A great 2-volume set on the UK telephone system, mine is the 1933
edition IIRC. They contain _complete_ schematics for telephone exchanges
(Well, OK, the circuit for each line is drawn once, not <n> times, but
you know what I mean). They were the books that finally let me understand
how telephgone exchanges work, and proved to me the dangers of giving a
simplified explanation (in that I'd read plenty of simplified books on
how telephone systems work and couldn't make any sense of them).
-tony
8:54 p.m.
New subject: Info on Chatsworth MR-500
I recently acquired a Chatsworth MR 500
card reader. I haven't been able to find
much documentation on it. Does anyone
have a manual or a pointer to some
technical documentation?
Cheers,
Dan
26 Sep
26 Sep
2:40 a.m.
Tony Duell wrote:
Yes, but I can't remember which end you put the slug at for which action
And slugged
relays, with a big metal ring in the coil. These either
delay opening or closing, but I can't remember which way round it works.
I believe (without running upstairs to look in 'Telephony' [1]) that you
can arrange for either a slow make or a slow release [1] A great 2-volume set on the UK telephone system,
mine is the 1933
edition IIRC. They contain _complete_ schematics for telephone exchanges
(Well, OK, the circuit for each line is drawn once, not <n> times, but
you know what I mean). They were the books that finally let me understand
how telephgone exchanges work, and proved to me the dangers of giving a
simplified explanation (in that I'd read plenty of simplified books on
how telephone systems work and couldn't make any sense of them).
Now, somewhere I have a very old book on telephony and telegraphy that
sounds very similar to that. At least, I hope I still have - after my
father went silent-key around 10 years ago, it seems that a few people
had some novel ideas about what belonged to them (his Bob Dylan lp
collection is long gone, for one thing). It had diagrams of the various
sections of the exchange, slightly simplified, and then another diagram
detailing how they go together (line finders, call routing, stuff like
that).
Gordon.
11:16 a.m.
On Sun, 26 Sep 2004, Gordon JC Pearce wrote:
Tony Duell wrote:
Yes, but I can't remember which end you put the slug at for which action
Normally I'd research this and have the detailed info before responding,
*especially* since I just recommended a lot of books on the Subject - but
after a cursory Google and skimmming thru the texts that are near to hand,
I can't find the actual detailed descriptions of the various
electromechanical 'delay' schemes.
From (faded) memory: If a copper ring is placed over the relay solenoid
near the end, it acts as a transformer, and when the current is removed,
it sets up a 'flux resonance' of sorts, acting to keep the magnetic field
alive - this action decays over a period determined by the various
parameters and physical layout of the relay - so the device delays it's
drop-out for X milliseconds after the excitation voltage drops.
NOW: I seem to recall that which 'end' of the coil (base or springs) has
an effect, and I *think* that the opposite effect - delayed pull-in - can
be gotten by using a soft iron ring in place of copper - the iron
magnetization current is different from the copper coil windings and thus
absorbs energy during the application of excitation current.
Like Tony, I have the Bell System Technical Journal, Vol. 1, No. 1
(1922) thru Vol 47 (1968)... BUT I haven't the time/space/energy right
now to go plowing thru all that just to look this up... maybe this
evening , *if* the project I'm working on is successful....
Cheers
John
And
slugged relays, with a big metal ring in the coil. These either delay
opening or closing, but I can't remember which way round it works.
I believe (without running upstairs to look in 'Telephony' [1]) that you
can arrange for either a slow make or a slow release [1] A great
2-volume set on the UK telephone system, mine is the 1933
edition IIRC. They contain _complete_ schematics for telephone exchanges
(Well, OK, the circuit for each line is drawn once, not <n> times, but you
know what I mean). They were the books that finally let me understand how
telephgone exchanges work, and proved to me the dangers of giving a
simplified explanation (in that I'd read plenty of simplified books on how
telephone systems work and couldn't make any sense of them).
Now, somewhere I have a very old book on telephony and telegraphy that sounds
very similar to that. At least, I hope I still have - after my father went
silent-key around 10 years ago, it seems that a few people had some novel
ideas about what belonged to them (his Bob Dylan lp collection is long gone,
for one thing). It had diagrams of the various sections of the exchange,
slightly simplified, and then another diagram detailing how they go together
(line finders, call routing, stuff like that).
Gordon.
12:08 p.m.
New subject: Relay computers - telephone type
another comment about telephone relays that I played with when I was twelve
(38 years ago) had a built in speed limitation. You could connect them up
in a buzzer fashion (power to coil through one of the contact sets) and the
relay would always make connect to the other pole of the switch and the
effect was to oscillate at around 10hz or so. You could not make them buzz
as you can normal relays. This guaranteed make capability was handy in
creating what I called a holding circuit. You could power the relay on and
use one contact set to connect power up to make the relay latch.
best regards, Steve Thatcher
6:47 p.m.
On Sun, 26 Sep 2004, John Lawson wrote:
On Sun, 26 Sep 2004, Gordon JC Pearce wrote:
According to the Engineering Relay Handbook, slugs at the armature end delay
both pickup and dropout, while slugs at the heel end have little effect on
pickup, but delay dropout. The slugs function as a shorted turn which will
generate an EMF on changing magnetic flux and resulting current will oppose
(Lenz's law) the applied field until the resistance in the slug cause the
current to decay.
Peter Wallace
Tony Duell wrote:
Yes, but I can't remember which end you put the slug at for which action
And
slugged relays, with a big metal ring in the coil. These either delay
opening or closing, but I can't remember which way round it works.
I believe (without running upstairs to look in 'Telephony' [1]) that you
can arrange for either a slow make or a slow release
24 Sep
24 Sep
2:57 p.m.
On Fri, 2004-09-24 at 07:39, Ade Vickers wrote:
If each relay needs, say, 25mA @ 6v to operate, then
the peak current
draw
of our R80 (as I shall call it) could be around 600A (I think). And
that's
before we've added memory, i/o, etc.
Last things first :-) the place to look for this is telco. They did
really for real. Most of them are 48V; it lowers current plus higher
voltages help with the inductive time constant thing (take a look at how
teletype loops are done; HV, a series resistor shortens the *effective*
time constant (eg. the time to reach 60mA in the tty case).
(either way), so I don't see how you could clock
the R80 at anything
faster
than around 40Hz; and you'd probably want to drop to 20Hz to be on the
safe
side.
First things second :-) doing a z80 might be silly, but I bet there's
architectures more amenable to relays.
Plus, if speed were you goal (probably not :-) asynchronous logic would
likely be better, at least within functional units. Setup inputs to a
net, when the output appears, there you go.
The same relays quote a typical lifetime of 10e7
operations; so at
20Hz, your R80 should last a little under 139 continuous hours of
operation
before relays started failing...
Telco!
Abd yes, wire-OR (or whatever, depending on conventions) is totally
appropriate.
I made a digital clock using relay T-type flipflops to do divide a
1-second timebase (pendulum! not made yet, substituted a 555 for
testing) 2, 4, 8, 16, 32nds of a minute, ANDed to get 60 in the usual
fashion, which drove a stepper 1-of-6, 1-of-10, and 1-of-12 decoders to
drive edge-lit display.
(Don't spoil the fun by pointing out it can be all done with the
steppers.)
You can actually *hear* ripple carry, which is cool.
It uses "sensitive" relays, a few mA at 36V I think. I never made the
pendulum timebase, nor finished the wiring for the display, as I
installed all the flops onto boards (redwood!) in a cardcage, realized
it needs to be re-laid out such that you can see all the relays at once.
I will eventually get around to it.
10:34 p.m.
Ade Vickers wrote:
...
I did some back-of-a-fag-packet calculations (i.e.
they might be
completely & utterly wrong, in which case I'd appreciate corrections) on
a relay computer...
Assume you want a Z80-type CPU. This has ~8k gates. Typically, it seems
to take 1 relay per input to implement any given gate. Now, I don't know
how many "x-input" gates there are in a Z80, so I'll assume that - on
average - it will require 3 relays/gate. Thus, we need ~24,000 relays to
implement the Z80.
...
i've read the other replies on the subject, but there is one failure in
your estimate that hasn't been mentioned that I noticed.
relays often have mutliple poles and multiple throws, rather than just a
single SPST type connection. as a result, one relay can be used on more
than one gate.
Imagine implementing this trivial logic:
y1 = a & b;
y2 = a & c;
you could use four relays where the "a" is wired to energize two of the
relays, while "b" and "c" inputs each energize one relay.
if you wire an "a" and "b" energized reley in series, there is a path
from in to out only if "a & b".
likewise, take the other pair of relays
and wire them in series to implement
"a & c".
Instead of four SPST relays, make one of them DPST (one electromagnet
that triggers two parallel but otherwise independent SPST switches). In
this case, the "a" input energizes this DPST relay, and the "b" and
"c"
relays are as before. Wire one pole of the "a" relay in series with the
"b" relay and the other pole of the "a" relay in series with the
"c"
relay. This implements the same logic but with three relays instead of
four.
That is a simple example, but imagine a more complex case with many
terms that include "a & (something)". In theory, only one relay is
needed for this part of all equations involving the "a &", limited only
by the mechanical problem of having so many poles.
There are other ways of sharing logic as well.
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