> I wonder how developers of computers came to idea to use binary numbers?

Logic gates[0]:

  A logic gate is an idealized or physical device
  that performs a Boolean function, a logical operation
  performed on one or more binary inputs that produces
  a single binary output. 

  ...

  In the real world, the primary way of building logic
  gates uses diodes or transistors acting as electronic
  switches.

0 - https://en.wikipedia.org/wiki/Logic_gate