http://csis.pace.edu/~bergin/polycalc/index.html

--
Mike W

You might start by studying some existing scientific calculators. The
instruction book will give you some hint as to what the various
functions do. You can experiment with numbers.  You can read up on the
names of the functions on the net.  A programmer's model converts
between hex, octal and possibly binary, and can do operations like
bitwise or, and xor.  You can probably ignore those for your project.

The thing that makes the scientific calculators interesting is the
ability to compute expressions and to store programs.  There are two
styles () and RPN. RPN are simpler to implement. They work much like
the JVM.

The catch is to understand the functions you will need to know at
least some elementary statistics, a little about complex math... A
scientific  calculator is almost a mini-course in math for engineers.

Some calculators now have graphing ability.  A simulated calculator
could do very well in this regard having way more pixels to play with.

Even if you can't afford a scientific calculator to experiment with,
you might find some popular model numbers and look them up on the
manufacturers web site. You may find PDF versions of the manuals.

I am not sure if it would be considered kosher to precisely emulate
some existing calculator, but if that is what your prof has in mind,
it would be nice to have an actual calculator to compare with.

You might talk some fellow students into lending their calculator's
for a few hours to experiment with, at least enough so that you could
compose a list of things you like and don't like about them. That
would help you in designing your own.

One of my pet peeves is entering large integers without seeing any
commas to break them into triples.

You probably won't be required to know WHY you would use a sinh
(hyperbolic sine) function, though were I in your shoes I would want
at least one sentence in my back pocket to cover that question.

This is a more open ended problem than usually assigned, more like the
real world..  Though it sounds grueling, you  will probably look back
on this time fondly since you were give so much free reign to study,
poke around and experiment.

Those multi-prof oral exams here are what PhD students go through.
This does not sound like a PhD level thesis.