Because the Ti 83/+/84+/SE are 16-bit calculators, doesn't that mean there can be something like 65536 shades of grey on the screen? Why 4? Why not at least 8? Is there a way to make an improved screen driver?

The bit width of the registers is not directly related to the shades of gray on the screen. In this instance, we are limited by the physics of the LCD. It cannot change from white to black instantaneously, and the driver IC only understands black and white. We fake it by switching between the two very quickly, but after a certain point, shades are indistinguishable (not to mention that the CPU isn't fast enough to blit new gray layers to the screen). The practical limit is about 4 shades leaving enough CPU time for a game or program; 8 shades eats up all the CPU time and needs extensive dithering to not flicker and look horrible.

Is there a way to possibly crack open the calculator and replace the Zilog CPU with a faster one? Would that f*ck up TI-OS?

Because of LCD and memory timing issues, not to mention gate propagation delay, there are limits to how far the built-in z80 can be overclocked, though it can be slightly overclocked. Obviously the 6MHz chips can, for the most part, go as far as 15MHz, and according to datasheets, even 20MHz and 25MHz (though TI did not implement those two higher speeds in anything). Unfortunately, only the earliest TI-84+/SE calculators has a discrete z80 CPU; the later models all use an ASIC created by TI that builds the CPU, RAM, and something I call a bus arbitrator (which actually does much more than that) into a single chip. You'd have to replace that entire chip, at which point you'd be better off creating entirely new insides.

Oh, okay. But, is it possible to make a new, faster ASIC chip out of several others?

I think that would make it a non-ti8x machine then. Even though we know quite a bit about how to communicate with the ASIC, we don't know enough to replace it, nor have the time, money, and equipment to do so. It would be much better to just run TIOS in an emulator on an embedded device.

This. Yes, it's possible, but at that point you're just interfacing the keypad, link port, LCD, and Flash with your own hardware, so you're better off interfacing that stuff directly to a powerful ARM SoC. Or powerful by TI-83+/84+ standards, anyway; it will still be slow and cheap in the grand scheme of things.

Okay.

I was also wondering,

is it possible to add a USB port to the body of the Ti-84+? You know, like one of those USB ports for a flash key/USB stick thing. I know that you can use USB drives, some mice and some keyboards with the usb8x driver, but you have to get a separate cord. Could we convince Ti to improve upon the Ti-84+ to add this feature, or can we make it ourselves?

Well, there's no circuitry involved in adapting the USB mini A/B port to a standard-sized type A, so it would be easy to build a type A port into your calculator with some trivial soldering. You'd just need a place to cut out the case and put the port. TI is not going to add that by any stretch the imagination; that's anathema to their goals of not having people be able to store a lot of information on their calculators. The tiny RAM would be trivial for them to do something about; the miniscule amount is choice.

I spliced a USB mini a and a USB A receptacle cable. Haven't used it yet :-\ But it is much easier than a hardware mod.

Why are Ti calcs so darned expensive from the company? What kind of circuitry is in them? I can get an iphone for less money than the Ti 89 Titanium!

You're paying for three things:

1) The LCD (it's hard to source those anymore)
2) The operating system (it took a lot of programmer-hours to write)
3) The monopoly TI has over the calculator market

For comparison, Casio sells a calculator with a fast 32-bit processor and a widescreen, dense color LCD for the same price as a TI-84+, so the hardware alone is absolutely not costing TI much.

Whoawhoawhoa WHOA.

You're saying that the Casio PRIZM is a 32-bit calculator? A color LCD screen? What a ripoff Ti has become! They're also installing faulty LCD drivers!

Oh, and about the 3D fractal thing and why Doom ports are sucky:

Is it more of a hardware limitation that the Ti-84+/SE can't really do 3D graphs? Or is it a software issue?

Well, you can get a carrier subsidized iPhone for less than that, as long as you agree to pay a carrier for usage every month. Look at unsubsidized pricing for a true comparison. Right now, Verizon want's $550 for an iPhone 4S @ full retail price.

Apple also sold, supposedly, 5 million iPhone 5's this weekend. That kind of volume get's you very interesting pricing, but tear down's are claiming a material price of $170 or so.

Here's a link http://www.eetimes.com/General/PrintView/4396862 to a nice teardown with a fair amount of deail.

Firstly, please do not double post. Second, the SH4a is a 16/32/64/128 bit CPU. The prizm doesn't use the 128 bit bus. Now, that 128 bus is for the FPU. Since the prizm lacks it, you don't get hardware 3D support.

Also, the method that Doom uses to blit the screen may still be using the syscall and can possibly be sped up by manually running a DMA transfer.

I wouldn't call the LCD drivers "faulty". They simply have limitations. Everything in engineering has limitations. It's just that you find these particular limitations too restrictive.

I mean, that if for instance, you install the Labyrinth game or the Maze3D game on your Ti-84+, and you reset the calc, the screen gets all screwed. There is a program to fix that, called ALCDFix, which thoroughly clears the LCD registers, if I'm not mistaken.

No, it adjusts the timing of the LCD to compensate for certain out-of-spec behavior. ALCDFix is one way to fix it, and (at the risk of constantly talking about it) Doors CS includes a menu that can tune the LCD settings similar to what ALCDFix foes.

Oh, cool! DCS can do ANYTHING!!!

It would be sweet if one were to make an LCD screen with 2x the resolution (but the same size) as the regular Ti-84+ screen. Then someone could make a special driver that converts all the regular Ti programs to work with the new screen, but it will also allow finer pics and the oppritunity to make really cool games specialized for that screen.