Which number represents the binary equivalent of octal 766?

To convert the octal number 766 to its binary equivalent, it's important to understand how octal (base 8) correlates with binary (base 2). Each octal digit can be represented by a set of three binary digits (bits).

Breaking down the octal number 766:

• The first digit is 7. In binary, 7 is represented as 111.

• The second digit is 6. In binary, 6 is represented as 110.

• The third digit is also 6, which is again represented as 110.

Now we combine these binary representations together:

• From the octal digit 7, we have 111.

• From the first 6, we have 110.

• From the second 6, we again have 110.

Putting it all together, we get:

111 (for 7) + 110 (for the first 6) + 110 (for the second 6) = 111110110.

This binary sequence is thus the equivalent of the octal number 766. Therefore, the correct answer is represented by the binary number 111110110. This methodical conversion from octal to binary underscores the relationship between the two