In which numbering scheme are there only two possible values for each digit?

In which numbering scheme are there only two possible values for each digit?

• A. Decimal
• B. Hexadecimal
• C. Binary
• D. Octal

Answer: (C)

The binary numbering scheme is characterized by having only two possible values for each digit, which are 0 and 1. This is the foundation of the binary system, where each digit represents an increasing power of 2. For example, in the binary number 101, the leftmost digit represents \(2^2\) (which is 4), the middle digit represents \(2^1\) (which is 2), and the rightmost digit represents \(2^0\) (which is 1). This simplistic structure allows computers to perform operations using just two states, corresponding to off (0) and on (1). In contrast, the decimal numbering system is based on ten digits (0 through 9), hexadecimal uses sixteen digits (0 through 9 and A through F), and octal employs eight digits (0 through 7). Each of these systems expands beyond the two-symbol framework of binary, thus confirming that binary uniquely supports the condition of having only two possible values per digit, making it the correct choice.

The binary numbering scheme is characterized by having only two possible values for each digit, which are 0 and 1. This is the foundation of the binary system, where each digit represents an increasing power of 2. For example, in the binary number 101, the leftmost digit represents (2^2) (which is 4), the middle digit represents (2^1) (which is 2), and the rightmost digit represents (2^0) (which is 1). This simplistic structure allows computers to perform operations using just two states, corresponding to off (0) and on (1).

In contrast, the decimal numbering system is based on ten digits (0 through 9), hexadecimal uses sixteen digits (0 through 9 and A through F), and octal employs eight digits (0 through 7). Each of these systems expands beyond the two-symbol framework of binary, thus confirming that binary uniquely supports the condition of having only two possible values per digit, making it the correct choice.