Express the number $100$ in binary system with $8$ bits. Assume that this $8-$bit dataword will be sent in two parts of $4$ bits with the C$(7,4)$ Hamming code in the relevant lecture note. For both $4-$bit pieces, a$)$ find and write the sent codeword $($either by looking at the table or by calculating the syndrome$)$ and b$)$ show the syndrome calculation on the receiver side, assuming that it is received without error.

$\backslash$table$[[$Datawords$,$Codewords,Datawords,Codewords$],[0000,00000,1000,10001],[0001,00011,1001,10010],[0010,00101,1010,10100],[0011,00110,1011,10111],[0100,01001,1100,11000],[0101,01010,1101,11011],[0110,01100,1110,11101],[0111,01111,1111,11110]]$