How many characters can the ASCII 7-bit binary data code differentiate?

The correct choice indicates that ASCII, which stands for American Standard Code for Information Interchange, is based on a 7-bit binary code. In a 7-bit binary system, each bit can represent two states: 0 or 1. Consequently, the number of unique combinations that can be created using 7 bits is calculated as 2 raised to the power of 7 (2^7).

This calculation results in 128 distinct combinations (2^7 = 128). Each of these combinations corresponds to a unique character or control command, which includes letters (both uppercase and lowercase), digits, punctuation marks, and control characters such as line feeds or carriage returns. Thus, ASCII can effectively differentiate and represent a total of 128 characters.

The other options incorrectly represent the number of characters. For instance, 64 corresponds to 6 bits (2^6), while 256 is indicative of 8 bits (2^8). Lastly, 512 would suggest 9 bits (2^9), leading to confusion in the context of ASCII, which is specifically defined within the framework of 7 bits.