Solution

To represent the 4-bit code 1101 into a 7-bit, even parity Hamming code, we first need to add 3 parity bits to the 4 data bits. The parity bits are chosen so that the total number of 1's in each group of bits (including the parity bit) is even.

Hamming Code:

Given data 1101

i.e. d1 = 1, d2 = 1, d3 = 0, d4 = 1

We can write:

P1 = d1 ⊕ d2 ⊕ d4 = 1 ⊕ 1 ⊕ 1 = 1

P2 = d1 ⊕ d4 ⊕ d3 = 1 ⊕ 1 ⊕ 0 = 0

P3 = d2 ⊕ d4 ⊕ d3 = 1 ⊕ 1 ⊕ 0 = 0

Then transmitted final code is P1 P2 d1 P4 d2 d3 d4 which is 1010101