You didn't state any additional requirements but this sounds like a school project. As already stated, a calculator, at least as we think of them today, is quite complex. Now, one might design and build something that will do the calcs but in more crude fashion. As I recall, before digital computers there we analog computers. Didn't they use simpler principles to add, subtract, multiply, divide, etc? You might explore something like this but for the output use a digital voltmeter for the output. If allowed, LEDs could indicate binary - though your description "digital" suggests decimal numerals.
As a simple begining you could 'add' by taking three 1.5 volt cells and put them in series to get the sum - 4.5 volts. To subtract you might reverse one - 3 volts minus 1.5 volts is 1.5 volts. An analog amp with a gain of 5 would serve to multiply the voltage - it will divide if it's less than one.
Just some thoughts. Good luck.