Let's solve the problem step by step. **Given:** - Code for station 1: `-1 -1 -1 1 1 -1 -1 -1` - Code for station 2: `1 1 1 1 -1 1 -1 1` - Received signal: `0 -2 0 2 0 0 2 2` We are to find the received bit value for station 2. --- ### **Step 1: Multiply received signal by station 2's code** \[ \begin{align*} &\text{Received signal:} & 0 & -2 & 0 & 2 & 0 & 0 & 2 & 2 \\ &\text{Station 2 code:} & 1 & 1 & 1 & 1 & -1 & 1 & -1 & 1 \\ \end{align*} \] \[ \begin{align*} 0 \times 1 &= 0 \\ -2 \times 1 &= -2 \\ 0 \times 1 &= 0 \\ 2 \times 1 &= 2 \\ 0 \times -1 &= 0 \\ 0 \times 1 &= 0 \\ 2 \times -1 &= -2 \\ 2 \times 1 &= 2 \\ \end{align*} \] So, the results are: `0, -2, 0, 2, 0, 0, -2, 2` --- ### **Step 2: Sum the results** \[ 0 + (-2) + 0 + 2 + 0 + 0 + (-2) + 2 = (0 - 2 + 0 + 2 + 0 + 0 - 2 + 2) = 0 \] --- ### **Step 3: Divide by code length (for averaging, if needed)** The code length is 8. \[ \frac{0}{8} = 0 \] --- ### **Step 4: Interpret the result** - If the result is **positive**, the bit is 1. - If the result is **negative**, the bit is 0. - If the result is **0**, the bit is ambiguous (possibly no data was sent). ### **Final Answer:** **The received bit value for station 2 is 0 (ambiguous, possibly no data sent).**

Let's revisit the problem with the correct code for station 2. --- ### Given: - Code for station 1: `-1 -1 -1 1 1 -1 -1 -1` - **Correct code for station 2:** `1 1 1 -1 1 -1 -1 -1` - Received signal: `0 -2 0 2 0 0 2 2` --- ### **Step 1: Multiply received signal by station 2's code** \[ \begin{align*} &\text{Received signal:} & 0 & -2 & 0 & 2 & 0 & 0 & 2 & 2 \\ &\text{Station 2 code:} & 1 & 1 & 1 & -1 & 1 & -1 & -1 & -1 \\ \end{align*} \] Calculations: \[ \begin{aligned} 0 \times 1 &= 0 \\ -2 \times 1 &= -2 \\ 0 \times 1 &= 0 \\ 2 \times -1 &= -2 \\ 0 \times 1 &= 0 \\ 0 \times -1 &= 0 \\ 2 \times -1 &= -2 \\ 2 \times -1 &= -2 \\ \end{aligned} \] Sequence of results: `0, -2, 0, -2, 0, 0, -2, -2` --- ### **Step 2: Sum the results** \[ 0 + (-2) + 0 + (-2) + 0 + 0 + (-2) + (-2) = -10 \] --- ### **Step 3: Determine the bit value** - Since the sum is **negative**, the bit for station 2 is **0**. --- ### **Final Answer:** **The received bit value for station 2 is 0.**