Convert the 32-bit binary Internet address 10000000 00001010 00000010 00011110 into dotted-decimal form. Choose the correct dotted-decimal representation.
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A148.20.2.30
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B164.100.9.61
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C210.20.2.64
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D128.10.2.30
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ENone of the above
Answer
Correct Answer: 128.10.2.30
Explanation
Introduction / Context: IPv4 addresses are 32-bit values typically shown in dotted-decimal notation as four octets. Converting from binary to dotted-decimal requires splitting the bit string into four 8-bit groups and converting each to base 10.
Given Data / Assumptions:
- Binary address: 10000000 00001010 00000010 00011110.
- Each group of 8 bits corresponds to one dotted-decimal octet.
- No subnet masks or class considerations are required—pure conversion only.
Concept / Approach: The algorithm: (1) split the 32 bits into four octets, (2) convert each 8-bit binary number to decimal using positional weights (128, 64, 32, 16, 8, 4, 2, 1), and (3) join with dots.
Step-by-Step Solution: Octet 1: 10000000 = 128.Octet 2: 00001010 = 8 + 2 = 10.Octet 3: 00000010 = 2.Octet 4: 00011110 = 16 + 8 + 4 + 2 = 30.Combine: 128.10.2.30.
Verification / Alternative check: Quick mental check: a leading 1 followed by 7 zeros is 128; small set bits in the second (8 and 2), third (2), and fourth (16+8+4+2) octets corroborate 10, 2, and 30 respectively.
Why Other Options Are Wrong: 148.20.2.30, 164.100.9.61, 210.20.2.64: Do not match the binary octet conversions.
None of the above: Incorrect because 128.10.2.30 is valid and matches exactly.Common Pitfalls: Mis-grouping bits (not on 8-bit boundaries) or arithmetic slips when adding powers of two. Always write out the weight positions to avoid errors.
Final Answer: 128.10.2.30