33 Hamming(7,4) Encoder/Decoder
33 : Hamming(7,4) Encoder/Decoder
- Author: Joseph Santhosh K,Noel Jose, Tinu P Mathew, Abhinav Kuruvila, Sahil K
- Description: Single-bit error correcting Hamming(7,4) encoder and decoder.
- GitHub repository
- Open in 3D viewer
- Clock: 10000000 Hz
Hamming(7,4) Encoder / Decoder
How it works
This project implements a Hamming(7,4) error-correcting code system. The circuit can encode 4-bit data into a 7-bit Hamming codeword and decode a received codeword while detecting and correcting a single-bit error.
The design operates in two modes controlled by the MODE input.
Encode mode
When MODE = 0, the chip encodes the input data bits into a 7-bit Hamming codeword.
Data bits are mapped as:
D1 = ui[0] D2 = ui[1] D3 = ui[2] D4 = ui[3]
The encoder generates three parity bits:
P1 = D1 ⊕ D2 ⊕ D4
P2 = D1 ⊕ D3 ⊕ D4
P4 = D2 ⊕ D3 ⊕ D4
The final codeword structure is:
P1 P2 D1 P4 D2 D3 D4
This 7-bit encoded word is produced on uo[6:0].
Decode mode
When MODE = 1, the chip interprets ui[6:0] as a received Hamming codeword.
The circuit computes a syndrome using parity checks:
S1 = C1 ⊕ C3 ⊕ C5 ⊕ C7
S2 = C2 ⊕ C3 ⊕ C6 ⊕ C7
S4 = C4 ⊕ C5 ⊕ C6 ⊕ C7
The syndrome {S4,S2,S1} indicates the position of a single-bit error.
If an error is detected, the corresponding bit is flipped to correct the codeword.
The corrected codeword is output on uo[6:0], and the error status is reported on uo[7].
How to test
Encoding test
- Set
MODE = 0 - Provide 4-bit data on
ui[3:0]
Example:
Input data
D = 1011
The encoder will generate the corresponding 7-bit Hamming codeword on uo[6:0].
Decoding test
- Set
MODE = 1 - Provide a 7-bit codeword on
ui[6:0]
Example:
Original codeword
1011101
Introduce an error (flip one bit):
1011001
Apply this value to the inputs.
The circuit will:
- detect the error
- correct the flipped bit
- output the corrected codeword on
uo[6:0] - set
uo[7] = 1to indicate an error was detected
External hardware
No external hardware is required.
- Input switches for
ui[7:0] - LEDs connected to
uo[7:0]to observe the encoded or corrected output.
IO
| # | Input | Output | Bidirectional |
|---|---|---|---|
| 0 | DATA0 | CODE0 | |
| 1 | DATA1 | CODE1 | |
| 2 | DATA2 | CODE2 | |
| 3 | DATA3 | CODE3 | |
| 4 | CODE_BIT4 | CODE4 | |
| 5 | CODE_BIT5 | CODE5 | |
| 6 | CODE_BIT6 | CODE6 | |
| 7 | MODE (0=ENCODE,1=DECODE) | ERROR_FLAG |