$($a$)$ Implement the following Boolean Expression using PLA i$.$e$.$ derive PLA program

table and draw its diagram showing internal paths and fuses using proper symbology.

$F_1(A,B,C)={\displaystyle \underset{?}{\overset{?}{}}}(0,2,4,6)$ and $F_2(A,B,C)={\displaystyle \underset{?}{\overset{?}{}}}(0,1,2,3)$

$3+2=5$

$($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$)$

$011001010101$