What is the 4B/5B encoding for the binary sequence 1101000011001101?
The Correct Answer and Explanation is:
The 4B/5B encoding for the binary sequence 1101 0000 1100 1101 is:
11010 11110 10110 1101
4B/5B encoding is a line coding scheme used in digital data transmission. It maps 4-bit groups (nibbles) into 5-bit codes that ensure there are enough transitions in the signal to maintain synchronization. This is important in systems like Fast Ethernet (100Base-TX) and Fiber Channel, where long runs of 0s or 1s can cause problems with clock recovery.
✳️ Step-by-step Encoding:
First, divide the input binary sequence into 4-bit nibbles:
1101 0000 1100 1101
Using the standard 4B/5B encoding table, encode each 4-bit group:
| 4-bit Input | 5-bit Output |
|---|---|
| 1101 | 11010 |
| 0000 | 11110 |
| 1100 | 10110 |
| 1101 | 11010 |
So, the 5-bit encoded sequence becomes:
11010 11110 10110 11010
This is your final encoded sequence.
✅ Why Use 4B/5B?
- Synchronization: Unlike simple NRZ (Non-Return to Zero) encoding, 4B/5B ensures that there are no long runs of 0s (or 1s), which could cause the receiver to lose synchronization.
- Efficient: The encoding overhead is small—only 1 extra bit per 4 bits (25% increase), which is more efficient than Manchester encoding, which doubles the bit rate.
- Error Detection: Not all 5-bit combinations are valid in 4B/5B. Invalid codes can be used to detect errors or control symbols.
🔚 Summary:
The 4B/5B encoding for the input binary sequence 1101000011001101 is:
11010 11110 10110 11010
This method improves synchronization and data integrity with only modest overhead, making it ideal for high-speed communication systems.
