8-bit PCs were derided as toys in the 1970s and with the benefit of hindsight people now scoff at that idea, but PCs really were much slower, less capable, and harder to program than minicomputers.
It was because of the crippling lack of ram and other cost-saving measures.
Having 1KB of ram (or less) on a single board computer like the KIM-1 wasn't an issue, because they were programmed in machine-code and didn't need to drive a screen.
But 1KB of ram on a low-cost microcomputer like the ZX80 was beyond painful. It takes 768 bytes for a full screen buffer, leaving just 384 bytes for the BASIC program, all it's variables and the interpreter state. And it took all the CPU time to drive the display. Actually running the program or even pressing a key would cause the screen to blank and desync.
Even on better micros that had ~4KB of ram, the scope of the BASIC program you could write was pretty limited.
Yes, but larger registers would need more physical force to manipulate. If you had smaller registers, you could have a higher gear ratio on the crank, allowing the machine to run faster for the same input force.
If they wanted to perform some particularly complicated instructions, then they might want a lower gear ratio instead. The obvious solution: install a gearbox and a shifter.
The Difference Engine was hand-cranked, but the Analytical Engine was intended to be steam-powered. The thing was going to be the size of a locomotive. Most of that was memory. As I've pointed out before, the big problem in the early days was affordable, fast memory. Babbage's design, at least one version, was to have the ability to store 1000 numbers of 40 digits each. So, 40,000 number wheels, with some kind of mechanism to bring them to the read/write station. Access time would probably have been measured in seconds.
The arithmetic unit wasn't the big part of the machine. It was roughly equivalent to a desktop mechanical desk calculator, after all.
Something similar appears to have happened with Babbage, where he started with a simple calculating device and, thinking about it more deeply, single-handedly came up with a Turing-complete design and was writing programs for it.
Desktop calculators existed long before Babbage. Leibniz built the first mechanical multiplier around 1673. Mechanical arithmetic was known. Babbage's contribution was the instruction decoder and control unit. Mechanical arithmetic was limited more by cost-effectiveness and reliability than by conception. The commercial breakthrough was cash registers, in the mid 1880s. First really cost-effective application. Babbage's machine might have been buildable, but not cost-effective.
A few years ago, there was some guy in the UK talking about an analytical engine build. But he never got very far. I'm surprised someone doesn't have one running in Minecraft or Unreal Engine.
I am sitting below a poster of Sydney Padua’s splendid cartoon of Plan 25, and her book and comics are the most entertaining way to learn a bit about Lovelace and Babbage http://sydneypadua.com/2dgoggles/comics/
"It's operated by a crank!!" "... Indeed." :-P
http://sydneypadua.com/2dgoggles/lovelace-and-babbage-vs-the...
Also, the 40 or 50 digit decimal number thing comes partly from not being clear on how to manage scaling "However, by inserting an imaginary divider between the same two figure wheels of all variable number columns, thus making all coefficients and numbers within the Store possess the same number of decimal places, decimals could be used."[1] So there was one decimal point location for all memory locations. Babbage apparently didn't include a general shift function, which is necessary for rescaling results. If you can shift to discard low order digits, as on mechanical desk calculators, you need maybe 10 digits, and a 20 digit product register, so you can multiply two 10-digit numbers and then round off or truncate the result. Without that, you need a lot more digits to avoid overflow. So close...
Useful programmable calculators from the 1970s had 20 to 100 memory locations, each capable of maybe 10 digits. A base Babbage machine with 200 digit wheels of memory, expandable to 1000, would probably have been feasible and moderately useful. Useful for cranking out navigation and gunnery tables, at least. Babbage's difference engine has about that much storage. So that was probably buildable as a minimum viable product.
[1] https://cs.stanford.edu/people/eroberts/courses/soco/project...
The Ingersoll dollar watch (1896), "The Watch that made the Dollar Famous", was probably the first high-volume mass produced product with part complexity and precision comparable to what Babbage needed. A few years later, the Computing-Tabulating-Recording company, the predecessor of IBM, was manufacturing the first commercial electromechanical computing devices in quantity. After that, there was steady progress.
Those were the days when New England was to the world what Guangdong is now.
If you can scale into a reasonable range for each data type, you don't need 50 digits. But that's an abstraction which came decades after Babbage.
Hiring someone to do the math would defeat the point. The idea was to eliminate human error when doing something like printing tables of common functions like sines or cosines.
A lot of effort went into designing a printer, as they couldn't have humans recording the results without re-introducing human error.