Final answer:
The information content of a string produced by XORing two random binary strings of length N remains N bits. The XOR operation is reversible and thus preserves the information content.
Step-by-step explanation:
When you have two strings of random binary digits, both N bits long, the information content of each is indeed N, assuming the strings are independent and uniformly random. The operation of XOR (exclusive or) will combine each corresponding bit from the two strings using the XOR truth table, resulting in another string of length N.
The information content of the resulting XOR’d string is still N bits. This is because the XOR operation does not create or destroy information; it merely transforms it. Each bit in the resulting string depends on the corresponding bits from the original strings in a way that is reversible – given one of the original strings and the XOR result, one can reconstruct the other original string. Therefore, the XOR operation preserves the information content.