Convert the unsigned octal number 67675 to hexadecimal.

Question

BlackTom AI · Accepted Answer

We start by understanding the task: convert the unsigned octal number 67675 into hexadecimal.
Option 1: 6FBD. This matches the correct conversion result, as will be shown by the step-by-step method below.
Option 2: 6FBE. The last digit differs from the expected hex result; small misalignment in the final nibble would produce a different last hex digit, so this is unlikely to be correct.
Option 3: 6FBC. Similar to option 2, but with a different final nibble; unless there was a carry or grouping error, this would not align with the proper binary representation from octal to hex.
Option 4: 6FAC. The final two hex digits here (AC) differ from the correct end of the sequence, indicating a mismatch in the binary grouping steps used to reach this value.
Option 5: None of these. Since a consistent, verifiable conversion exists, asserting that none of the listed options are correct would require ruling out all prior options, which is typically not the case when a standard octal-to-hex conversion is performed correctly.

Now, let’s perform the conversion to see which option aligns with the actual result. Convert octal digits to binary in groups of three bits: 6->110, 7->111, 6->110, 7->111, 5->101, giving the full binary string 110111110111101.
To convert to hexadecimal, group the binary digits in sets of four from the left. Since there are 15 bits, pad with a leading zero to get 16 bits: 0110111110111101.
Splitting into nibbles yields: 0110 1111 1011 1101, which correspond to hex digits: 6 F B D. Therefore, the correct hexadecimal representation is 6FBD.

In summary, the critical steps are: (a) map each octal digit to 3 binary bits, (b) concatenate, (c) pad to a multiple of 4 bits, (d) group into 4-bit chunks, and (e) translate each nibble to its hex equivalent. With these steps, option 1 aligns with the computed value, while the other options fail to match the properly derived hex digits.

CSE-12-02 Quiz 3 : Sequential Circuits, Signed Numbers, Decoders, Multiplexers

Convert the unsigned octal number 67675 to hexadecimal.

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