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Consider a simple code C for error detection and correction. Each codeword in C consists of 2 data bits $[d_1, d_0]$ followed by check bits $[c_2, c_1, c_0]$. The check bits are computed as follows: $c_2 = d_1+d_0, \: c_1=d_1 \text{ and } c_0=d_0$, where '+' is a modulo-2 addition.

1. Write down all the codewords for C
2. Determine the minimum Hamming distance between any two distinct codewords of C