Hamming codes are used for error detection and correction in communication and memory systems. Error detection and correction capability is incorporated in these codes by inserting extra bits into the data word. Addition of one parity bit can detect odd number of bit flips, but no error correction is possible with one parity bit. A (7,4) Hamming code has 4 bits of data but 7 bits in total, including the 3 parity bits. It can detect two errors and correct one error. This code can be constructed as follows: If we denote data bits as d₄d₃d₂d₁, the encoded code word would be d₄d₃d₂p₄d₁p₂p₁, where p₄, p₂, and p₁ are the added parity bits. These bits must satisfy the following conditions for even parity:

p₄ = d₂ XOR d₃ XOR d₄;……………………….(1)
p₂ = d₁ XOR d₃ XOR d₄;……………………….(2)
p₁ = d₁ XOR d₂ XOR d₄;……………………….(3)
When the 7 bits are received/decoded, an error syndrome S₃S₂S₁ is calculated as follows:
p₄ XOR d₂ XOR d₃ XOR d₄ = S₃;……………………….(4)
p₂ XOR d₁ XOR d₃ XOR d₄ = S₂;……………………….(5)
p₁ XOR d₁ XOR d₂ XOR d₄ = S₁;……………………….(6)
The syndrome indicates which bit is wrong. For example, if the syndrome is 110, it indicates that bit 6 from right end (i.e., d₃) has flipped. If S₃S₂S₁ is 000, there is no error. 

(a) Is there any error in the code word 0110111? If yes, which bit? What was the original data? What must be the corrected code word?
(b) How will these 6 equations get modified for odd parity? Write the 6 equations for odd parity.
(c) Write a Verilog module for error detection without using tasks. The inputs to the module are the 7-bit encoded data word and the type of parity, and the output is the syndrome. The type of parity is encoded as 0 for odd parity and ₁ for even parity.

module error_detector(data, PARITY, Syndrome)
 {
 }

(d) Modify the Verilog module in (c) to use Verilog tasks. Write required Verilog task(s) that will generate the error syndrome given the code word. The input to the task is data, and output is the syndrome. You have to call necessary task(s) for each type of parity.
task error_p(data, Syndrome)
 {
 }