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Why is it not Turing complete? | 756 comments | Create New Account
Comments belong to whoever posts them. Please notify us of inappropriate comments.
Why is it not Turing complete?
Authored by: wharris on Friday, July 20 2012 @ 06:38 PM EDT
First let's make sure we're talking about the same thing. When I am describing a
simple calculator, I mean something like the one at:
http://www.casio.com/products/Calculators_%26_Dictionaries/Basic/HS-8V/


There is no CPU inside that calculator. There is no software to change. There is
no mechanism to cause such a device to output Dit Dot Space.

Did I misunderstand your original post? If so, I'm sorry. I am not familiar with
the AL1, but the 8008 is a general purpose CPU and Turing-complete.

[ Reply to This | Parent | # ]

I think this is in reference to only add/subtract/multiply/divide
Authored by: jesse on Saturday, July 21 2012 @ 08:38 AM EDT
where these operations are strictly done within an arithmetic logic unit.

With only these four capabilities, the calculator is not Turing complete (no
test, no loop, no decision table, no status other than the answer).

Nearly all calculators with the above capabilities, are turing complete as they
actually have to have sequencers, a rom for directions. They are/were
implemented using even simpler operations - add, complement, and shift. The
subtract is via adding a twos complement (complement one number, add 1, add the
other number). Shifting can be considered a fast multiply by 2, but becomes more
necessary when implementing multiplication or division.

To make such a calculator Turing complete requires adding a sequencer, test
circuits, a loop capability, I/O (minimum to the display, from the keypad).

And trying to directly connect the base registers (accumulator) to the display
or keypad (operand register) just doesn't work well - BCD arithmetic is rather
messy from the the circuit point of view.

[ Reply to This | Parent | # ]

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