Convert the unsigned octal number 67675 to hexadecimal.

Question

BlackTom AI · Accepted Answer

To start, I will outline the conversion task and then evaluate each answer option step by step.
Option 1: 6FBD. This is the candidate we know matches the correct hex value after proper conversion, but I will verify through the full process to confirm.
Option 2: 6FBE. If any small misstep occurs in the binary-to-hex grouping or a single bit error happens, this adjacent hex value could appear as a plausible near-miss. We’ll see why it does not arise from the exact octal input.
Option 3: 6FBC. Similar to Option 2, it differs by one hex bit; checking whether a single-bit difference could result from a common grouping mistake helps illustrate why it is wrong.
Option 4: 6FAC. This diverges more noticeably in the lower hex digits, suggesting a mismatch in the corresponding binary sequence derived from octal digits.
Option 5: None of these. This would be correct only if none of the listed hex values matched the conversion result, which we will test against the actual conversion process.
Now, performing the actual conversion: an octal number converts to hex via its binary representation, since each octal digit maps to exactly three binary bits. The octal number 67675 becomes:
- 6 -> 110
- 7 -> 111
- 6 -> 110
- 7 -> 111
- 5 -> 101
Concatenating these three-bit groups yields the binary string: 110111110111101.
This binary string has 15 bits. To group into 4-bit hex digits, pad on the left with a zero to make 16 bits: 0 110111110111101 -> 0110 1111 1011 1101.
Now, convert each 4-bit group to hex: 0110 -> 6, 1111 -> F, 1011 -> B, 1101 -> D. Therefore, the hexadecimal representation is 6FBD.
With this in mind:
- Option 1 (6FBD) matches the derived result exactly, so it is the correct hex equivalent.
- Option 2 (6FBE) would require the binary tail to end in 1110 instead of 1101, which does not align with the computed 1101 tail from 7 and 5 in octal.
- Option 3 (6FBC) would end in 1100, again not matching the 1101 tail from the last two octal digits, so it is incorrect.
- Option 4 (6FAC) changes more than just the final bits, indicating a mismatch in the lower nibble and thus not corresponding to the original binary sequence.
- Option 5 (None of these) would only be true if none of the listed values matched, but since 6FBD exactly matches the conversion, this option is false.
In summary, the exact binary packing of the octal digits 67675 yields 0110 1111 1011 1101, which converts to hexadecimal 6FBD, matching Option 1 precisely.

CSE-12-02 Quiz 4 : Number Conversions

Convert the unsigned octal number 67675 to hexadecimal.

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