Which binary code is less information-dense than binary numbers with the same number of bits?

The reason BCD, or Binary-Coded Decimal, is less information-dense than binary numbers with the same number of bits lies in its representation of decimal numbers. In BCD, each decimal digit is represented by its own binary sequence consisting of four bits. This means that for each decimal digit, an additional binary sequence is required, leading to more bits being used overall.

For example, to represent the decimal number 95 in binary, you would use eight bits (binary 01011111). However, in BCD, the same number would take a total of eight bits as well, but it's inefficiently segmented into two separate four-bit segments: 0009 and 0101, which correspond to 9 and 5, respectively. Thus, while both representations can use the same number of bits to express a decimal number, BCD's approach leads to a much less efficient encoding of information, particularly when considering larger numbers.

In contrast, formats like Gray Code, ASCII, and EBCDIC are designed for different uses. Gray Code is often used in error correction and minimizing digital errors, focusing on minimizing the change between consecutive values, and ASCII and EBCDIC are character-encoding schemes that facilitate text display and processing rather than numerical