To determine the octal equivalent of the binary number $(10110101)_2$, we can proceed as follows:

1. Convert the binary number to octal by grouping its digits into sets of three, starting from the right (since each octal digit represents three binary digits).

Given binary number: $10110101$

Let's add an extra 0 at the beginning to complete the grouping in sets of three:

• $010 \, 110 \, 101$

2. Convert each group to its octal equivalent:

   • $010$ in binary is $2$ in octal.
   • $110$ in binary is $6$ in octal.
   • $101$ in binary is $5$ in octal.

3. Combine the results to get the final octal number:

   • So, $(10110101)_2 = (265)_8$.

Answer:

The correct answer is (c) 265.

Would you like further explanation on any step or have any other questions?

Here are some related questions that might interest you:

1. How do you convert a binary number to hexadecimal?
2. What is the process to convert an octal number to binary?
3. How would you convert a decimal number directly to octal?
4. Can you explain the relationship between binary, octal, and hexadecimal bases?
5. How can you verify your answer when converting from binary to octal?

Tip: When converting binary numbers to octal, group the binary digits in sets of three from right to left.