Odd Parity Hamming code
- The given number is 1011 which holds 3 bits of 1's. Therefore, it represents the Odd Parity.
- The given number is 4-bits code hence, there are 3 parity bits p1, p2, and p3.
- This is also called Hamming (7, 4) code, which is a linear error-correction methodology that encodes 4-bits of data into 7-bits, by addition of 3 (P1, P2, P3) parity bits.
- Therefore, the resultant 7-bits hamming code looks as follows:
|Resultant Hamming Number||P1||P2||d1||P3||d2||d3||d4|
Here, d1, d2, d3, and d4 represent the 4-bits of code 1011.
d1 = 1, d2 = 0, d3 = 1, and d4 = 1
The value of P1, P2, and P3 calculated as follows:
$P1 = d1 \oplus d2 \oplus d4$
$P2 = d1 \oplus d4 \oplus d3$
$P3 = d2 \oplus d4 \oplus d3$
$P1 = d1 \oplus d2 \oplus d4 = 1 \oplus 0 \oplus 1 =0$
$P2 = d1 \oplus d4 \oplus d3 = 1 \oplus 1 \oplus 1 = 1$
$P3 = d2 \oplus d4 \oplus d3 = 0 \oplus 1 \oplus 1 = 0$
Now, the final Resultant Hamming Code looks as follows:
Odd parity Hamming code for 1011 is 0110011