What is the best explanation for why digital data is represented in computers in binary?

Digital data is represented in computers using binary because it's easier, cheaper, and more reliable to construct machines that operate on binary states. Binary uses just two symbols, 0 and 1, which can easily correspond to the two possible states of a physical device, like an electrical circuit being either off (0) or on (1).

This simplicity allows for more straightforward designs in hardware, reducing the complexity and potential for errors. For example, switching between two states is less prone to failure than dealing with multiple states or levels that would be required in systems based on other number systems, such as decimal or hexadecimal. Furthermore, using binary reduces the likelihood of noise interference that could misinterpret intermediate states, thus enhancing reliability in data processing and storage.

The other options, while they may have elements of truth, do not capture the main reason for binary's dominance in computing. Other number systems may be theoretically flexible, but they complicate hardware design and increase costs. Early use of binary for secret codes is an interesting historical note but not the primary driver for its use in computing today. The statement that it’s impossible to build non-binary computers is misleading since there have been attempts with other bases, but they are generally impractical for the reasons mentioned