1. **Problem 1:** Compute the bitwise AND of $1011\ 0110$ and $1100\ 1100$. Bitwise AND compares each bit of two numbers and returns 1 only if both bits are 1. $$\begin{aligned} &1011\ 0110\\ &1100\ 1100\\ &\text{AND}\rightarrow 1000\ 0100 \end{aligned}$$ So, the result is $1000\ 0100$. 2. **Problem 2:** Perform bitwise XOR on $0101\ 1010$ and $0011\ 1100$. Bitwise XOR returns 1 if the bits are different, 0 if they are the same. $$\begin{aligned} &0101\ 1010\\ &0011\ 1100\\ &\text{XOR}\rightarrow 0110\ 0110 \end{aligned}$$ So, the result is $0110\ 0110$. 3. **Problem 3:** Find the output of ~$5$ in an 8-bit system. First, write 5 in 8-bit binary: $0000\ 0101$. Bitwise NOT (~) flips all bits: $$\sim 0000\ 0101 = 1111\ 1010$$ This is the two's complement representation of $-6$. 4. **Problem 4:** Write a program to check if a number is odd or even using bitwise OR. The key idea: For any integer $n$, $n \& 1$ checks the least significant bit. If $n \& 1 = 1$, $n$ is odd; else even. Example in Python: ```python n = int(input()) if n & 1: print("Odd") else: print("Even") ``` This uses bitwise AND, which is the correct operator for this check. Bitwise OR cannot be used to check odd/even directly. **Summary:** - Problem 1 result: $1000\ 0100$ - Problem 2 result: $0110\ 0110$ - Problem 3 result: $1111\ 1010$ (which is $-6$ in decimal) - Problem 4: Provided a program using bitwise AND to check odd/even.