Convert the binary number 10111101 into its equivalent octal representation:
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Answer: B. 275
Explanation
To convert binary 10111101 to octal, group bits in threes from the right: 10 (2), 111 (7), 101 (5), resulting in 275. Grouping binary digits into triads starting from the least significant bit allows direct translation into base-eight octal number equivalents. Converting each three-bit binary combination yields the respective octal digits two, seven, and five in correct positional order. Binary number systems use base two with digits zero and one, whereas octal number systems use base eight with digits ranging from zero to seven. Digital systems engineering frequently utilizes octal and hexadecimal notations as shorthand representations for lengthy binary machine code sequences. Standard number base conversion rules require grouping bits in powers of two to transition smoothly between binary and higher-radix systems.
An octal value of 675 is mathematically incorrect and results from improper grouping or faulty binary-to-octal digit calculation procedures. An octal value of 572 is wrong because the binary bit groupings do not evaluate correctly to the digits five, seven, and two. An octal value of 573 is incorrect because the least significant binary bit combination evaluates to five rather than three.
- Subject
- Engineering
- Category
- Electrical Engineering
- Topic
- —
- Difficulty
- medium
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