What is the octal representation of the hexadecimal number AF?

The octal representation of the hexadecimal number AF is 257.

To convert a hexadecimal number to octal, we first need to convert it to binary and then from binary to octal. Hexadecimal is a base-16 number system, while octal is a base-8 number system.

Let's start with the hexadecimal number AF. In hexadecimal, A represents 10 and F represents 15. The binary representation of A (10 in decimal) is 1010 and the binary representation of F (15 in decimal) is 1111. Therefore, the binary representation of AF is 10101111.

Next, we convert this binary number to octal. Binary numbers are grouped by threes from right to left to convert to octal. So, 10101111 becomes 010 101 111. Now, we convert these binary groups to their octal equivalents. 010 in binary is 2 in octal, 101 in binary is 5 in octal, and 111 in binary is 7 in octal. Therefore, the octal representation of the binary number 10101111 is 257.

So, the octal representation of the hexadecimal number AF is 257. This process of conversion is fundamental in computer science, as different number systems are often used in different areas of computing. For example, hexadecimal is commonly used in programming and web design, while octal is used in systems programming and when working with file permissions in Unix-like operating systems. Understanding how to convert between these systems is a key skill for any computer science student.