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The problem asks to generate a code word using the Hamming code method for the data "0101." It also asks to detect and correct any errors in the received code word "0101010."

### Step 1: Generating the Hamming Code
Hamming code is a linear error-correcting code that adds redundancy bits to detect and correct single-bit errors in data transmission. Here's how it's done:

For a 4-bit data word "0101", we will need to add redundancy (parity) bits at positions that are powers of 2 (i.e., positions 1, 2, 4, 8, etc.). For this 4-bit data, we will add 3 parity bits at positions 1, 2, and 4.

### Step 2: Arranging Data and Parity Bits
The positions of the parity bits are marked as "P", and the data bits are placed in the remaining positions:

| Position   | 1  | 2  | 3  | 4  | 5  | 6  | 7  |
|------------|----|----|----|----|----|----|----|
| Bit        | P1 | P2 | D1 | P3 | D2 | D3 | D4 |

We now place the data bits (0101) in the positions labeled D:

| Position   | 1  | 2  | 3  | 4  | 5  | 6  | 7  |
|------------|----|----|----|----|----|----|----|
| Bit        | P1 | P2 | 0  | P3 | 1  | 0  | 1  |

### Step 3: Calculating Parity Bits
- **P1 (covers bits 1, 3, 5, 7):**
  \[
  P1 = D1 \oplus D2 \oplus D4 = 0 \oplus 1 \oplus 1 = 0
  \]
- **P2 (covers bits 2, 3, 6, 7):**
  \[
  P2 = D1 \oplus D3 \oplus D4 = 0 \oplus 0 \oplus 1 = 1
  \]
- **P3 (covers bits 4, 5, 6, 7):**
  \[
  P3 = D2 \oplus D3 \oplus D4 = 1 \oplus 0 \oplus 1 = 0
  \]

Now, placing the parity bits into their respective positions, the final Hamming code (encoded word) is:

| Position   | 1  | 2  | 3  | 4  | 5  | 6  | 7  |
|------------|----|----|----|----|----|----|----|
| Bit        | 0  | 1  | 0  | 0  | 1  | 0  | 1  |

The generated Hamming code is **0100101**.

### Step 4: Detecting the Error in the Received Code Word
The received code word is given as **0101010**. We will check each parity bit to determine if there is an error.

#### Recalculate the Parity Bits for the Received Code Word:
- **P1 (bits 1, 3, 5, 7):**
  \[
  P1 = D1 \oplus D2 \oplus D4 = 0 \oplus 1 \oplus 0 = 1
  \]
- **P2 (bits 2, 3, 6, 7):**
  \[
  P2 = D1 \oplus D3 \oplus D4 = 1 \oplus 1 \oplus 0 = 0
  \]
- **P3 (bits 4, 5, 6, 7):**
  \[
  P3 = D2 \oplus D3 \oplus D4 = 1 \oplus 1 \oplus 0 = 0
  \]

The error syndrome (binary number formed by the incorrect parity checks) is **101**, which equals **5** in decimal. This means there is an error in position 5.

### Step 5: Correcting the Error
The bit in position 5 is currently 1, so we flip it to 0. The corrected code word becomes **0100010**.

Thus, the original transmitted code word was **0100101**, and the corrected version of the received word is **0100010**.

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Let me know if you'd like further clarification or have any questions.

Here are five related questions to explore further:
1. How does the Hamming distance help in detecting multiple-bit errors?
2. Can Hamming code correct more than one error in a received message?
3. What is the difference between even and odd parity in Hamming codes?
4. How would the Hamming code method change if the data word had more than 4 bits?
5. How does the position of parity bits in Hamming code vary with different data lengths?

**Tip**: Always double-check parity calculations when working with error-correcting codes to avoid missing subtle mistakes.

Generate code word for following data using Hamming code method: 0101. If receiver receives the code word 0101010, find the error in it, if any.

Learn how to generate a code word using the Hamming code method for the data 0101. This detailed solution also shows how to detect and correct an error in the received code word 0101010.

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