Which of the following statement is/are correct? I. (1071)10 = (2057)8 II.…

To convert (1071)10 to Octal (base 8), we divide the decimal number by 8 and track the remainders:

1. 1071 / 8 = 133 with a remainder of 7

2. 133 / 8 = 16 with a remainder of 5

3. 16 / 8 = 2 with a remainder of 0

4. 2 / 8 = 0 with a remainder of 2

Reading the remainders from bottom to top, we get (2057)8 .

Statement I is correct.

To convert (1AF)16 to Decimal (base 10), we use the positional weights of hexadecimal, where A = 10 and F = 15:

1. 1 X 162 = 1 X 256 = 256

2. A X 161 = 10 X 16 = 160

3. F X 160 = 15 X 1 = 15

4. Total: 256 + 160 + 15 = 431

Since (1AF)16 = (413)10, the statement (1AF)16 = (413)10 is incorrect.

Statement II is incorrect.