X is a 16-bit signed number. If the n’s complement representation of X is(F76A)16. The n’s complement representation of ( 8 * X) is

The question seems to be incomplete as it does not specify the value of 'n' in n's complement. The n's complement is a method of representing negative numbers in a system that only allows for positive numbers. The value of 'n' determines the method used to calculate the complement.

However, assuming that 'n' is 2 (which is a common case), we can proceed as follows:

1. Convert the hexadecimal number F76A to binary. The binary equivalent of F76A is 1111 0111 0110 1010.

2. Since X is a 16-bit signed number and its 2's complement is given, it means that X is a negative number (because the sign bit is 1).

3. To find the original number X, calculate the 2's complement of F76A. The 2's complement of a binary number is found by inverting the digits (1's complement) and then adding 1. The 2's complement of 1111 0111 0110 1010 is 0000 1000 1001 0110.

4. Now, to find the 2's complement of 8*X, first multiply X by 8. When you multiply a binary number by 8, you essentially shift the bits to the left by 3 places. So, 0000 1000 1001 0110 becomes 1000 1001 0110 0000.

5. Finally, calculate the 2's complement of the result to get the 2's complement representation of 8*X. The 2's complement of 1000 1001 0110 0000 is 0111 0110 1010 0000.

6. Convert the binary result back to hexadecimal to get the final answer. The hexadecimal equivalent of 0111 0110 1010 0000 is 76A0.

So, the 2's complement representation of 8*X is (76A0)16.

Please note that this solution assumes that 'n' is 2. If 'n' is not 2, the method to calculate the n's complement will be different.