Which of the following is exact equivalent of given binary number in Octal…
2023
Which of the following is exact equivalent of given binary number in Octal Number? (101110001011) 2
- A.
(232023)8 / (232023)8
- B.
(A8A)8 / (A8A)8
- C.
(5613)8 / (5613)8
- D.
(3165)8 / (3165)8
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Correct answer: C
Method: convert the binary number to octal by grouping bits in threes from the right and converting each group to an octal digit.
Write the binary number: 101110001011
Group into three bits from the right: 101 110 001 011
Convert each 3-bit group to its octal digit: 101 → 5, 110 → 6, 001 → 1, 011 → 3
Combine the digits to get the octal number: (5613)8
Note: Octal digits range from 0 to 7, so any representation containing 8 or letters (for example 'A') is invalid in base 8.
Answer: (5613)8