Why do computers represent data using binary numbering?

Because the underlying devices used to represent the data are two-state devices: on or off. Vacuum tubes, transistors, magnetic toruses, magnetic disks, optical disks, are some of those devices. For all of them, it's most convenient and reliable to store information in arrays of on-or-off states.Why do computers represent data using binary numbering?
Communication within the computer is via on/off wires/signals. The 1s and 0s are merely representions of those on/off signals.Why do computers represent data using binary numbering?
Because computers all operate using a type of transistor called a flip-flop. These flip-flops have two positions which we label as on and off or 1 and 0 which is the same system that binary use. A single microchip can have billions of flip-flops built into it and that is how data is stored, by positioning these flip-flops in the 1 or 0 position.





To make binary much more useful computer us opamps and later other type of transistors to channel the binary code using boolean logic to do more advanced math calculations.





Just as a fun fact Binary was invented in India around 800 BC. Boolean logic wasn't invented until the 1890's in England.
Because it makes the circutry simpler and more reliable. You have either an off or an on--anything in between has to be one or the other. The more space between valid answers the easier it is to deal with interference.