Difficulty: Easy
Correct Answer: Correct
Explanation:
Introduction / Context:This question checks the most fundamental property of binary notation: regardless of how addition is carried out internally (with carries and intermediate logic), the written result in base-2 uses only the symbols 0 and 1.
Given Data / Assumptions:
Concept / Approach:Binary numbers are expressed with two symbols. During addition, each bit position computes a sum bit (0 or 1) and possibly a carry to the next position. No matter how many carries propagate, each output digit remains 0 or 1. The process may widen the word (e.g., an extra most-significant bit), but the alphabet of symbols does not change.
Step-by-Step Solution:
Add bitwise with carry: sum_bit = A xor B xor carry_in (0 or 1).Compute carry_out = majority(A, B, carry_in) (0 or 1).Concatenate all sum_bits (and a final carry if present) to form the base-2 result, which uses only 0 and 1.Verification / Alternative check:Example: 1011 + 0111 = 10010. Even with multiple carries, the digits in the result are still only 0s and 1s.
Why Other Options Are Wrong:
Incorrect: Contradicts the definition of base-2 representation.Only correct without carry: Carries do not introduce new symbols; they only extend width.Ambiguous for signed numbers: Signed encodings (two's complement) still use 0/1 digits.Insufficient context: The statement is precise and standard.Common Pitfalls:Confusing intermediate analog voltages or adder internals with the symbolic numeric result.
Final Answer:Correct
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