1. The problem is to fill in the missing number system conversions in the table. 2. For row 1 and 2, Decimal is 255 and Binary is 111111110. However, 111111110 in binary equals $\sum_{i=1}^8 1\times 2^{i} = 510$, not 255. Assuming the binary is correct, Decimal should be 510. 3. Convert Binary 111111110 to Octal: Group bits in 3 from right: 111 111 110 111 (binary) = 7 (octal), 111 = 7, 110 = 6 So Octal = 776 Convert Binary 111111110 to Hex: Group bits in 4 from right: 1111 1110 1111 = F, 1110 = E Hex = FE 4. For row 3, Binary is 111111110, Octal is 377, Decimal is 1111110. Check Octal 377 to Decimal: $3\times 8^2 + 7\times 8^1 + 7\times 8^0 = 3\times 64 + 7\times 8 + 7 = 255$ This does not match Decimal 1111110, so likely Octal 377 corresponds to Decimal 255. 5. For row 4, Decimal is 10101010, Hex is 16A4F. Convert Hex 16A4F to Decimal: $1\times 16^4 + 6\times 16^3 + 10\times 16^2 + 4\times 16^1 + 15\times 16^0 = 65536 + 24576 + 2560 + 64 + 15 = 92751$ So Decimal should be 92751, not 10101010. Convert Decimal 10101010 to Binary: $10101010_{10} = 1001101001010100101010_2$ 6. For row 5, all values are missing. 7. For row 6, Hex is 2048. Convert Hex 2048 to Decimal: $2\times 16^3 + 0 + 4\times 16^1 + 8 = 8192 + 0 + 64 + 8 = 8264$ Convert Decimal 8264 to Binary: $8264_{10} = 10000000101000_2$ Convert Decimal 8264 to Octal: $8264_{10} = 20050_8$ 8. For row 7, Binary is 111110101100. Convert Binary 111110101100 to Decimal: $1\times 2^{11} + 1\times 2^{10} + 1\times 2^9 + 1\times 2^8 + 1\times 2^7 + 0 + 1\times 2^5 + 0 + 1\times 2^3 + 1\times 2^2 + 0 + 0 = 3964$ Convert Decimal 3964 to Octal: $3964_{10} = 7554_8$ Convert Decimal 3964 to Hex: $3964_{10} = F74_{16}$ Final filled table: 1. Decimal: 510, Binary: 111111110, Octal: 776, Hex: FE 2. Decimal: 510, Binary: 111111110, Octal: 776, Hex: FE 3. Decimal: 255, Binary: 111111110, Octal: 377, Hex: FF 4. Decimal: 92751, Binary: 101101010010011111, Octal: 535237, Hex: 16A4F 5. All missing 6. Decimal: 8264, Binary: 10000000101000, Octal: 20050, Hex: 2048 7. Decimal: 3964, Binary: 111110101100, Octal: 7554, Hex: F74