Binary-to-decimal conversion method: “A binary number can be converted to decimal by summing the decimal weights of all positions that contain a 1.” Decide if this description is correct.

Introduction / Context:Understanding positional weights is foundational in number systems. The conversion from binary to decimal hinges on the idea that each bit represents a power of 2, and that the decimal value is the sum of the weights for bits set to 1. This question validates mastery of that principle.

Given Data / Assumptions:

• Binary digits (bits) have weights 2^0, 2^1, 2^2, ... from right to left.
• Only positions with bit value 1 contribute to the sum.
• Unsigned interpretation is assumed unless specified otherwise.

Concept / Approach:For any binary string b_n ... b_2 b_1 b_0, the decimal value is Σ(b_k * 2^k). When b_k = 1, that power of 2 adds to the total; when b_k = 0, it contributes nothing. This direct sum is the standard, exact method for conversion.

Step-by-Step Solution:

Verification / Alternative check:Example: 101101₂ = 12^5 + 02^4 + 12^3 + 12^2 + 02^1 + 12^0 = 32 + 8 + 4 + 1 = 45. This matches the decimal interpretation, confirming the rule.

Why Other Options Are Wrong:

• Incorrect: Denies the fundamental positional weight definition.
• Only for unsigned / up to 8 bits / endianness: These caveats do not change how binary-to-decimal conversion is computed; sign conventions affect interpretation, not the arithmetic of weights.

Common Pitfalls:Mislabeling bit positions (starting at 1 instead of 0), forgetting to include a weight, or confusing endianness (byte order) with numeric value; endianness is a storage layout issue, not a mathematical one.

Final Answer:Correct