What is the binary representation of the octal number 756?

The binary representation of the octal number 756 is 111 101 110.

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 consists of eight digits from 0-7. The binary number system is base 2, consisting of two digits, 0 and 1.

The octal number 756 can be broken down into three individual digits: 7, 5, and 6. Each of these digits can be converted into a binary number.

The binary equivalent of the octal digit 7 is 111. The binary equivalent of the octal digit 5 is 101. The binary equivalent of the octal digit 6 is 110.

Therefore, when we replace each octal digit in 756 with its binary equivalent, we get 111 (for 7), 101 (for 5), and 110 (for 6).

So, the binary representation of the octal number 756 is 111 101 110.

Remember, when converting from octal to binary, each octal digit corresponds to a three-digit binary number. This is because the largest number you can represent with three binary digits is 7 (which is 111 in binary), and the octal system is based on powers of 8, so it fits perfectly with the 3-digit binary representation.

This method of conversion is straightforward and can be applied to convert any octal number to binary. It's a useful skill to have, especially for computer science students who often work with different number systems.