What is the binary representation of the octal number 542?

The binary representation of the octal number 542 is 101100010.

To convert an octal number to binary, each octal digit is replaced by its binary equivalent. The octal number system is base 8, meaning it uses eight symbols (0-7), while the binary system is base 2, using two symbols (0 and 1).

The octal number 542 can be broken down into three digits: 5, 4, and 2. Each of these digits can be converted into a three-digit binary number. The binary equivalents for 5, 4, and 2 are 101, 100, and 010 respectively.

So, to convert the octal number 542 to binary, replace each octal digit with its binary equivalent:

5 becomes 101,
4 becomes 100,
2 becomes 010.

When you put these together, you get the binary number 101100010.

Remember, when converting from octal to binary, each octal digit corresponds to a three-digit binary number. This is because the largest digit in octal (7) requires three binary digits to represent (111).

So, the binary representation of the octal number 542 is 101100010. This method can be used to convert any octal number to binary.