1. **Problem Statement:** Convert the decimal number 330 (base 10) to binary (base 2), then to octal (base 8), and finally to hexadecimal (base 16). 2. **Step 1: Convert from decimal (base 10) to binary (base 2).** - Use repeated division by 2, recording remainders. - 330 ÷ 2 = 165 remainder 0 - 165 ÷ 2 = 82 remainder 1 - 82 ÷ 2 = 41 remainder 0 - 41 ÷ 2 = 20 remainder 1 - 20 ÷ 2 = 10 remainder 0 - 10 ÷ 2 = 5 remainder 0 - 5 ÷ 2 = 2 remainder 1 - 2 ÷ 2 = 1 remainder 0 - 1 ÷ 2 = 0 remainder 1 - Reading remainders from bottom to top: $330_{10} = 101001010_2$ 3. **Step 2: Convert from binary (base 2) to octal (base 8).** - Group binary digits in sets of 3 from right to left: 101 001 010 - Convert each group to octal: - 101 = 5 - 001 = 1 - 010 = 2 - So, $101001010_2 = 512_8$ 4. **Step 3: Convert from octal (base 8) to hexadecimal (base 16).** - Convert octal to binary by converting each octal digit to 3 binary digits: - 5 = 101 - 1 = 001 - 2 = 010 - Combined binary: 101001010 - Group binary digits in sets of 4 from right to left: 0001 0100 1010 (add leading zeros to make full groups) - Convert each group to hexadecimal: - 0001 = 1 - 0100 = 4 - 1010 = A - So, $512_8 = 14A_{16}$ **Final answers:** - $330_{10} = 101001010_2$ - $101001010_2 = 512_8$ - $512_8 = 14A_{16}$