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Many early Texas Instruments calculators used a Z80 processor. The Z80 is notoriously limited when it comes to mathematical calculators. For example, while it can do addition, multiplication must be implemented as addition in a loop. While this may be fine for early home computers, it seems like it would be a terrible choice for a machine designed for floating point arithmetic. Other contemporary processors such as the 68k were fully capable of integer multiplication and division, and floating point arithmetic could be implemented with reasonable efficiency even with no FPU.

Why did early TI calculators, especially the TI-8x series, use the Z80?

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    The relevant TI line seems to have started with the TI-81 in 1990 and been superseded by the TI-89 in 1998, supposing that helps anybody with an answer. It'll end up being something about availability as a synthesisable core* and/or power consumption and/or size, I'm sure. (* that's why the Atari Lynx has a 6502, officially. The 68000 wasn't available for purchase as a synthesisable core, so couldn't be embedded within the custom chipset. Also it'd have been too large.) – Tommy Jun 23 '18 at 23:02
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    Many calculators used special purpose CPUs optimised for decimal arithmetic. For example the Sharp SC61860 ESR-H or HP Saturn family. They were very slow but very very low power. – TEMLIB Jun 24 '18 at 1:05
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    For acalculator, you are not looking for integer arithmetics at all. Multiplication or division opcodes don't help. You want floating point features, that had to be implemented in software back then. You seem to state the Z80 is bad at that - But with no reasoning behind. – tofro Jun 24 '18 at 9:23
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    As already have been mentioned, chances are that TI-xx routines work in DECIMAL mode, rather than binary. Two consequences are: 1. CPU is likely to have hardware decimal mode (both Z80 and 68k fit) and 2. CPU-native multiplication/division commands (that work in binary mode) render useless. Probably that is also the part of question, the other part being simply the price of Z80 vs the price of 68k. – lvd Jun 24 '18 at 16:35
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    @tofro, there was at least one calculator that did integer arithmetic. I still use the one that I purchased in 1984. – Solomon Slow Mar 30 at 23:33
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The Z80 is notoriously limited when it comes to mathematical calculators.

Not more than CPUs used in calculators before. Like any other device a pocket calculator is about sufficient speed, not maximum speed. A Z80 is more than capable to do several hundred up to a few thousand flotingpoint operations per second - way more than the average calculator user ever can use.

Other contemporary processors such as the 68k were fully capable of integer multiplication and division

Which doesn't make a big difference in real life application. Producing a square root after 1/1000 second instead of 1/100 second (or a two seconds) doesn't matter for the user, does it?

Not to mention that a 68000 wasn't much faster than a Z80 with comparable technology. The main advantage of 16 (or 32) bit processors wasn't about speed, but addressable memory.

and floating point arithmetic could be implemented with reasonable efficiency even with no FPU.

Not so much better than a Z80. Especially when considering the increased price.

Be serious, would you - and more important millions of parents - have been willing to pay like triple the price, just to have a different CPU, one the user (normally) never sees? For a speed increase 99.99% of all users never experience in real life?

Why did early TI calculators, especially the TI-8x series, use the Z80?

Seriously, why shouldn't they? The Z80 is a wide available CPU with many variations, has great tool collection, and most importantly is available for ASIC integration. Which is an incredible argument for system builders (like TI). Integration is the main source of cost savings. Including CPU, RAM, ROM, I/O and drivers in one package saves a fortune.

In fact, when looking at this new generation of TI calculators using a standard - and non-TI - CPU the question is rather

Why did they switch to a standard CPU based design

Until then TI calculators used CPUs based on special calculator designs. Well proven, all in house developed and handled. Diverting from such a well proven path is a rare decision.

For TI the answer might have been that it was maybe no longer possible to deliver the increased requirements with sometimes 20+ year old designs. To make it work replacement had to be not only capable but also cheap. Dirt Cheap. A complete restart like this costs a lot of money for development and production ramp up. And the resulting product must of course meet customer expectations - not the least of them will be the price. Sure, a new, way more capable model can fetch more money, but not a premium, as it still must be within school budget for most parents.

As a result the component must be not only available but also low priced. Selecting a well proven CPU that is available at a real low price per unit (when going for the expected sales) is a must. Sure, it must be capable to do the job. But only the job. There is no budget for something fancy only engineers may dream of.

In case of these machines, using a Z80 might have beaten even the use of CPU cores TI already produced at the time. That alone should be telling, shouldn't it?

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    Somehow reading a question of you on RC makes me think that you're not an average user. Wellcome if the .01% :) So tell me, would your parents have been willing to spend three times as much money on a calculator back then - and if yes, would you considere that average again? – Raffzahn Jun 24 '18 at 0:29
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    Three times? Maybe not. But remember, people using the graphing calculator for, well, graphing did have to wait several seconds for simple calculations, and upwards of a minute for more complicated ones. I remember one time it took several seconds for each pixel to be drawn when evaluating some biochemistry equation from a school textbook. For a simple scientific calculator with an 8 digit display, I can totally understand using dirt cheap components. But these systems were designed to do very complex equations with a large number of steps and map them to a dot matrix LCD in real time. – forest Jun 24 '18 at 0:31
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    @CortAmmon per e.g. xkcd.com/768 TI might not be the best company at taking advantage of price improvements. – Tommy Jun 24 '18 at 1:04
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    @forest I think your use case requires something more substantial than a $100 calculator. For me as a trigonometry student, the graphs I needed took less than 5 seconds to plot. – snips-n-snails Jun 24 '18 at 4:22
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    @Tommy Seems like they're pretty good at taking advantage of price improvements, in that they get to watch their profit margins expand with no significant engineering work. ;) TI and HP have both gone ARM with the Nspire and Prime respectively, since that's the ASIC/SOC of choice these days. Casio has used things like SH4, SH3, and even 8086 for a few models. – db2 Jun 24 '18 at 22:04
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Some important clarifications to the question.

First, TI-80 was based on proprietary CPU and TI-89 was 68000-based, so formally the question is wrong.

Second, both Z80-based and 68k-based TI calculators used decimal floating point format. Therefore, even the extensive binary multiplication and division capabilities of 68k wouldn't help much in BCD and decimal operations.

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