How does a calculator work?

We posed this question to maths teacher Jeffrey Zilahee from mathgurus.info...

杰弗里-我们都知道计算器这些fast little machines that can do calculations in incredible speed and have served to make humanity more computationally exact species, but exactly, how do they work? Well, whether you're talking about a scientific, financial graphing, or even a calculator on your phone, they all work in a similar fashion. In a nutshell, calculators just like their big brother, the computer, work by understanding everything in terms of two states. We call this binary and specifically, those two states are given as either a zero or a one. So, when we press buttons on a calculator, those buttons are connected to sensors that send electrical currents to the integrated circuitry of a calculator. This circuitry contains transistors that build up a logical framework for solving any given calculation, and the more transistors present, the more advance the functionality of the calculator is likely to be. Transistors use electricity to be in an on-state indicated by a one and off, indicated by a zero. So when a calculator wants to add two numbers it first converts those numbers into binary. For example, a four would be represented as 1-0-0 and a two would be represented as 1-0. From there, the process of addition is dictated by each column either summingto 0, 1, or two 1s, in which case a one would go into the next column since calculators cannot comprehend a 2. Once the calculator has the answer since it is in binary, it turns on a series of lines and/or pixels to create the visual match of the number that we understand which is decimal or as mathematicians call it - base 10. Part of the reason why calculators are so quick is because at their core, they're relying on electrical impulses which travel at the speed of light.

Diana - So, calculators, much like computers, translate everything into binary or base 2 because it allows numbers to be translated into electrical signals that are either on '1' or off '0.' To display an answer, it then sends this information to its LCD screen and as those of you with any sort of LCD TV monitor or clock may know that these displays work by placing a voltage across a layer of molecules which are layered between filters and the changing voltage will make these liquid crystals appear opaque or transparent.