Convert the unsigned octal number 67675 to binary.

Question

BlackTom AI · Accepted Answer

To begin, I will restate the task: convert the unsigned octal number 67675 to its binary representation, using the standard 3-bit mapping for each octal digit.
First, recall the direct octal-to-binary conversion rule: each octal digit corresponds to exactly three binary bits. This means we can convert digit-by-digit without performing more complex arithmetic.
Looking at the digits of 67675 in octal, we have the sequence 6, 7, 6, 7, 5.
- The octal digit 6 converts to binary as 110.
- The octal digit 7 converts to binary as 111.
- The next octal digit 6 again converts to binary as 110.
- The following 7 converts to binary as 111.
- Finally, the octal digit 5 converts to binary as 101.
Assembling these 3-bit groups in order yields: 110 111 110 111 101.
Now, evaluate the provided options:
- Option A: 110 111 110 111 101 — This matches the exact concatenation of the per-digit binary equivalents, so it correctly represents 67675 in binary.
- Option B: 111 011 110 111 101 — Here the first group is 111 instead of 110, which would imply a different first octal digit, so this option misrepresents the conversion.
- Option C: 111 010 110 101 111 — This sequence disrupts the grouping pattern and does not align with any standard per-digit conversion for 6, 7, 6, 7, 5, indicating an incorrect mapping.
- Option D: 110 010 110 101 011 — This option alters several groups compared to the correct mapping, showing improper conversions for at least some digits.
- Option E: None of these — Since the first option exactly matches the correct per-digit binary equivalents, this choice is contradicted by the valid result.
In summary, the correct approach is to translate each octal digit independently into its 3-bit binary form and then concatenate the results. Any deviation in the bit groups indicates a misapplication of the octal-to-binary mapping, which is why the other options fail to represent 67675 accurately.

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

Convert the unsigned octal number 67675 to binary.

View Explanation

Log in for full answers

Similar Questions

Convert the following hexadecimal numbers to decimal. A4 = [Fill in the blank] 7C = [Fill in the blank] (20)16 = [Fill in the blank] (100)16 = [Fill in the blank] (8000)16 = [Fill in the blank] (100000)16 = [Fill in the blank]

What is the hexadecimal equivalent of the decimal number 26?

convert the decimal number 201 to hexadecimal.

convert the hexadecimal number 19A to decimal.

Question textPlease convert the binary number 0b110011100 to hexadecimal number 0xAnswer[input]CorrectThe correct answer is: 19CMark 1.00 out of 1.00 (without leading 0s，不填高位0)

Convert the unsigned octal number 67675 to hexadecimal.

Convert the unsigned octal number 67675 to hexadecimal.

In a consumer society, many adults channel creativity into buying things

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler