Given a binary number X 11010101001011101, find the binary representation of X * 8 (X multiplied by 8).

1. Break Down the Problem

To find the binary representation of $X \times 8$, we will convert the multiplication by 8 into a simpler form using binary shifts.

2. Relevant Concepts

In binary, multiplying a number by $2^n$ can be achieved by shifting the binary digits to the left by $n$ positions. Therefore, multiplying by $8$ (which is $2^3$) involves shifting the binary representation of $X$ three places to the left.

3. Analysis and Detail

The given binary number $X$ is: $X = 11010101001011101$ Now, we will shift this number 3 positions to the left to obtain $X \times 8$.

1. Shift the binary number:
   • Original number: $11010101001011101$
   • After shifting left by 3 positions: $11010101001011101000$

4. Verify and Summarize

To verify, note that the left shift adds three zeros to the end of the binary number without changing the other digits. The final binary representation of $X \times 8$ is correct as we have accurately shifted the original number.

Final Answer

The binary representation of $X \times 8$ is: $11010101001011101000$