1. **Problem Statement:** Calculate the 8-bit checksum code using the sum complement method for the data bytes: 0x72, 0x40, 0x34, 0x36, 0xF1, 0x92, 0x77, 0x06. 2. **Method:** The sum complement checksum is calculated by summing all bytes, taking the least significant 8 bits of the sum, and then finding the one's complement (bitwise NOT) of that result. 3. **Step 1: Convert hex to decimal and sum:** $$\text{Sum} = 0x72 + 0x40 + 0x34 + 0x36 + 0xF1 + 0x92 + 0x77 + 0x06$$ Calculate each in decimal: $$0x72 = 114,\ 0x40 = 64,\ 0x34 = 52,\ 0x36 = 54,\ 0xF1 = 241,\ 0x92 = 146,\ 0x77 = 119,\ 0x06 = 6$$ Sum: $$114 + 64 + 52 + 54 + 241 + 146 + 119 + 6 = 796$$ 4. **Step 2: Take least significant 8 bits:** Since 8 bits can represent values from 0 to 255, take modulo 256: $$796 \mod 256 = 796 - 3 \times 256 = 796 - 768 = 28$$ 5. **Step 3: Find the one's complement:** One's complement of 28 (decimal) is: $$255 - 28 = 227$$ 6. **Step 4: Convert back to hexadecimal:** $$227_{10} = E3_{16}$$ **Final checksum code:** $\boxed{0xE3}$