Binary and Hexadecimal Representation

When we want to represent a number in binary form, we follow a simple process. We divide the number by 2 and record the remainder. Then, we divide the quotient by 2 again, record the remainder, and continue this process until the quotient becomes 0. The binary representation is obtained by arranging the remainders in reverse order.

For example, let's take the number 185. When we divide 185 by 2, we get a quotient of 92 and a remainder of 1. Next, when we divide 92 by 2, we get a quotient of 46 and a remainder of 0. Continuing this process, we eventually get the binary representation of 185 as (10111001)₂.

When it comes to representing a number in hexadecimal form, the process is somewhat similar. We divide the number by 16 and record the remainder. If the remainder is greater than 9, we use letters A-F to represent it in the hexadecimal system.

For instance, for the number 185, when we divide it by 16, we get a quotient of 11 and a remainder of 9. Since 9 is greater than 9, we represent it as B in hexadecimal. Therefore, the hexadecimal representation of 185 is (B9)₁₆.

By understanding these processes, we can easily convert numbers from decimal to binary and hexadecimal forms. It's a fun way to explore different number systems and expand our mathematical knowledge!