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In a book my Michio Kaku (called Physics of the Future) he makes the claim that a chip in a birthday card that sings a song is more powerful than all the computers the allied had in 1945.

Now, I don't say I believe this claim, but my question is: Why use a relatively powerful chip for a simple task like this? Or am I underestimating the task of playing a song when opened?

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Humans can hear up to 20 kHz, which means the processor must be able to send a minimum of 20000 samples to the speaker each second. Additionally, raw uncompressed audio is huge, and so it's usually compressed. And decompressing in real time is a nontrivial task... – Mooing Duck Mar 18 '14 at 21:16
@MooingDuck - Good point about compression. About frequency: To get 20 kHz, you need a sampling rate of at least 40 kHz. Fortunately, the low fidelity of a greeting card does not demand frequencies anywhere near what the human ear can hear. – Wayne Conrad Mar 18 '14 at 23:09
The point is probably that the cheapest microcontroller you can buy today is more powerful than what the allied had in 1945. Which is quite believable, because clock frequencies where very low then, and memory was an even bigger problem. But still much better than computing by hand. BTW, Zuse's mechanical Z3 was clocked at 5Hz. – starblue Mar 19 '14 at 21:12

Why use a relatively powerful chip for a simple task like this?

Economics. It's the same reason you'd send email spam, which requires a very high technology, instead of mass-mailing letters, which requires basically no technology. Computers and the internet, despite the high technology involved, are so ubiquitous that sending electronic spam is cheaper than actually mailing letters.

While email requires computers and the internet, which are each very expensive things in themselves, the incremental cost of sending an email is very nearly zero, once all the infrastructure is in place.

Sending a physical letter, on the other hand, requires a real human to carry a real letter printed on real paper and put it in a real mailbox. The cost of the paper alone makes the incremental cost of this method higher.

It's the same with a birthday card. Once the infrastructure is in place (semiconductor fabrication facilities, the IC masks, etc), the incremental cost of making that device is very low. Furthermore, the technology is such that the same device can play any number of songs, and in fact may be usable for applications beyond birthday cards. As such, the development costs are amortized to nearly zero, and the incremental costs are very low.

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First, the power the chip in the card is irrelevant. What matters is its cost in large quantities.

Second, your logic for claiming it is a relatively powerful is flawed. You show that it is powerful relative to computers 70 years ago, but that is irrelevant since those computers weren't alternate choices to the manufacturer of the birthday card. To decide relatively powerful you have to compare to other choices available at the time. Given that, it is not relatively powerful.

Given the volume, the chips in greeting cards are probably not general purpose computers or microcontrollers, so comparing them to computuers - of any era - is misleading. In high volume, a custom chip just to play a short song stored in a ROM is quite simple and cheap by today's standards. Less relavantly, it is also NOT very "powerful" (however that is really measured) compared to simple and low cost computing chips of today.

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None of the Allied computers in 1945 were general purpose either. Most of them were custom cryptanalysis machines. – Brian Drummond Mar 18 '14 at 21:11
@Brian: Good point. That makes it even less meaningful to compare "power" of these chips, whatever that is supposed to mean anyway. – Olin Lathrop Mar 18 '14 at 22:23

Why is it hard to believe that claim? the closest thing the allies had to a "computer" in WW2 was the Bombe to crack enigma messages. It was electro-mechanical and the size of a shed and was VERY VERY slow. It was Turing work that spawned computer science and the concept of a turing machine.

compared to today the uC in such cards are trivial and are the type that are taught at Uni or before.

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Not only the bombes, but also Colossus - en.wikipedia.org/wiki/Colossus_computer – peterG Mar 18 '14 at 14:59

There are a number of chips which are designed for things like melodic birthday cards and contain mainly counters, some ROM, and a little bit of state-control logic. While there are no doubt some cards which contain microcontrollers, most cards do not. Cards which play digitized audio likely have a quantity of ROM which exceeds by orders of magnitude anything that would have been practical in World War II, though of course a WWII-era phonograph record or optical soundtrack could store vastly more music than a typical card; cards that play a sequence of notes generally have only a small amount of ROM (probably under 256 bytes).

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While a synthesized "electronic music box" can be pretty simple, anything using recorded audio probably uses a perceptual compression codec, and playing that back has a moderate degree of complexity. – Chris Stratton Mar 18 '14 at 15:20
@ChrisStratton: Historically, they haven't. The process requirements for ROM are pretty simple, so a 1mm2 chip chich contains ROM and little else may be cheaper than a 0.5mm2 chip which contains a smaller ROM and a microcontroller to decode it. – supercat Mar 18 '14 at 15:30

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