What is the octal representation of the binary number 10101010?

The octal representation of the binary number 10101010 is 252.

To convert a binary number to its octal equivalent, we group the binary digits into sets of three, starting from the rightmost (least significant) digit. If the number of binary digits is not a multiple of three, we add zeros to the left (most significant) side to complete the group.

The binary number 10101010 can be grouped into three sets as 001 010 101 010. Now, we convert each group into its octal equivalent. The octal equivalent of 001 is 1, 010 is 2, and 101 is 5. Therefore, the octal representation of the binary number 10101010 is 1252.

However, it's important to note that the leading zero in the octal number is usually dropped, so the final octal representation is 252. This conversion process is a fundamental concept in computer science, as it allows us to represent binary data in a more compact and readable format.

Remember, the key to converting binary to octal is to group the binary digits into sets of three, then convert each group into its octal equivalent. This method is straightforward and efficient, making it a useful tool for computer scientists and programmers.