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Hamming Codes: Detecting and Correcting Errors Hamming code is a set of error-correction codes that can be used to detect and correct bit errors that can occur when computer data is moved or stored. Hamming Codes-Construction Begin with a 4 bit string. Recall that a bit is a digit which is either zero or one. Call the string a_1 a_2 a_3 a_4. Three check digits, c_1, c_2, and c_3, will be attached to the 4 bit string to produce a 7 bit string. C_1, C_2, and c_3 are chosen as follows: C_1 = 0 if a_1 + a_2 +a_3 is even C_1 = 1 if a_1 + a_2 + a_3 is odd C_2 = 0 if a_1 + a_3 + a_4 is even C_2 = 1 if a_1 + a_3 + a_4 is odd C_3 = 0 if a_2 + a_3 + a_4 is even C_3 = 1 if a_2 + a_3 + a_4 is odd Example: Construct the Hamming code word corresponding to the 4 bit string 0101 a_1 + a_2 + a_3 = 0+1+0 is odd so c1 = 1 a_1 + a_3 + a_4 = 0 + 0+ 1 is odd so c2 = 1 a_2+ a_3 + a_4 = 1 + 0+ 1 is even so c3 = 0 The Hamming code word corresponding to 4 bit string 0101 is 0101110. Find the Hamming code for string 0011