The ignition switch of an automobile is discrete — it has definite states — but there are usually more than two states (off, running, start, acc...) A button on a hand calculator is a binary device. It is either on or off. Ordinarily it is "off." When you push it, it is "on." It springs back to "off" when you release it, which is different from a toggle switch, but it still is a binary device.
There are many advantages to binary. Here are four (somewhat overlapping) important reasons for using binary:
These characteristics of binary were realized by Claude Shannon, a mathematician at Bell Telephone Laboratories. His 1948 paper A Mathematical Theory of Communication is the foundation of information theory and much of computer science.
Which is easier to build: