Which cipher encrypts the plain text digit (bit or byte) one by one?

Classical cipher is a broad historical category (e.g., Caesar, Vigenere) and does not specifically define the unit-by-unit encryption mechanism being described.

Block cipher encrypts data in fixed-size chunks (e.g., 128 bits at a time as in AES), not one digit at a time, which is the opposite of the described behavior.

Modern cipher is a general category term encompassing both block and stream ciphers and does not specifically describe unit-by-unit encryption.

Stream ciphers process plaintext digit by digit - typically one bit or one byte at a time - by XORing each unit with a corresponding value from a pseudo-random keystream. This makes them suitable for real-time data transmission where data arrives continuously. RC4 is a well-known example of a stream cipher operating on bytes.