Question Discussion & Solution

The correct answer is The correct answer is A: 2. The binary system (also known as base-2) uses only two distinct digits, 0 and 1. The value of each position in a binary number represents a power of 2, starting from \( 2^0 \) for the rightmost digit, then \( 2^1 \), \( 2^2 \), and so on, moving to the left..

🔑 Key Points

• The binary number system is a base-2 system, meaning it uses two symbols to represent numbers: 0 and 1.
• In any positional number system, the value of each digit is determined by its position and the base of the system.
• For binary numbers, each position represents a power of 2. For example, the number \( 1011_2 \) can be broken down as \( (1 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) \).
• This is analogous to the decimal system (base-10), where each position represents a power of 10 (e.g., ones, tens, hundreds are \( 10^0, 10^1, 10^2 \) respectively).

📄 Additional Information

• Binary is the fundamental language of digital computers and electronics because it's easily represented by two distinct states, such as 'on' or 'off', 'high' or 'low' voltage. Other number systems like octal (base-8, uses powers of 8) and hexadecimal (base-16, uses powers of 16) are also used in computing as compact representations of binary values.