What is the hexadecimal representation of the octal number 643?

The hexadecimal representation of the octal number 643 is 1C3.

To convert an octal number to hexadecimal, we first need to convert the octal number to binary, and then convert the binary number to hexadecimal.

Let's start with the octal number 643. Each digit in an octal number represents three binary digits, so we can convert each digit separately. The binary representation of 6 (in octal) is 110, of 4 is 100, and of 3 is 011. Therefore, the binary representation of the octal number 643 is 110100011.

Next, we convert this binary number to hexadecimal. Each digit in a hexadecimal number represents four binary digits, so we group the binary number into sets of four, starting from the right. If necessary, we can add leading zeros to the leftmost group to make it a set of four. In this case, we don't need to add any zeros, and we get the groups 1101 and 00011.

The hexadecimal representation of 1101 (in binary) is D, and of 00011 is 3. Therefore, the hexadecimal representation of the binary number 110100011 (and thus of the original octal number 643) is D3.

However, it seems there was a mistake in the grouping. The correct grouping should be 0001 and 1100011. The hexadecimal representation of 0001 (in binary) is 1, and of 1100011 is C3. Therefore, the correct hexadecimal representation of the binary number 110100011 (and thus of the original octal number 643) is 1C3.

This process might seem a bit complicated at first, but with practice, it becomes easier. It's also worth noting that there are online tools that can do these conversions for you. However, understanding the process is important for a solid understanding of number systems in computer science.