$($a$)$ Implement the following Boolean Expression using PLA ie derive PLA program table and draw its diagram showing internal paths and fuses using proper symbology. F$($A$.$B$.$C$)-\backslash$Sigma $(0,2,4,6)$ and F:$($A$.$B$.$C$)=(0,1,2,3)3+2-51$

$($b$)$ A $12-$bit Hamming code word containing $8$ bits of data and $4$ parity bits is read from memory. What was the original $8-$bit data word that was written into memory if the $12-$bit word read out is as follows$($Assume that only a single bit error can occur, if any$)$

$011001010101$