In practice, this calculator may only be good to win bets: "I bet you that my calc here with 9 buttons can do everything yours can do."
The full power of ND1 within 9 keys, where two are button "sliders" that have their function change (interactively) as you slide your finger over the button. So, you select from the four given operators by placing your finger where you know it is on the button, or sliding there. Similarly, you select numbers 0 thru 9 by sliding over the number slide button. The dot key provides, of course, any of the functions ND1 has--on the generous 4 soft keys.
Hence the ability to outdo most calculators. Moebius function, anyone? Plotting the butterfly? Solving a hard Project Euler problem involving 4 million prime number? Let them try.
Kinda fun. Maybe.
How it works:
 An empty button of size 1/4 of full width.
Function is @soft, the usual soft-key designation, as in ND1.
 ., edit is a button for showing menus and doing the edit function upon long-press (2nd function).
 @by_function is a button, taking up 1/2 of the available width, whose text varies by function.
Its function is to @calc, which is the code name for the enter key.
So the text this button will show is either = or up-arrow or ENTER, depending on RPN vs. ALG, Modern vs. Classic setting. Defaults to = here, as the calc is elsewhere on the definition page set to non-RPN.
 <-, drop
A combined backspace, drop button. 1/4 space allotment.
slide (1, 2, 3, 4, 5, 6, 7, 8, 9, 0) is a button that displays whatever is in parentheses, depending on where the user has his finger.
Its function is to push the selected content onto the stack. (In this case the numbers 0-9.)
slide (/, -, +, *) works the same way. Note that what the button displays can be distinct from what it pushes. (The division sign is differently represented.)
If you populate the menus with all 500 functions, this calc can do anything ND1 can, via the 4 soft-keys.