When 2 N-bit binary numbers are added, the sum will contain at most:
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When 2 N-bit binary numbers are added, the sum will contain at most:
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Answer: B. B) N+1 bits
Adding two N-bit integers can produce a maximum value of 2*(2^N - 1) = 2^(N+1) - 2, which requires at most N + 1 bits to represent without overflow.
Step-by-step Derivation:
Step 1: Maximum value of an N-bit unsigned binary number is 2^N - 1.
Step 2: Sum of two such numbers = (2^N - 1) + (2^N - 1) = 2^(N+1) - 2.
Step 3: To represent this number, ceil(log2(2^(N+1) - 1)) = N + 1 bits are required.