$1.$ Implement the following functions using a single $16\backslash$times $3$ ROM. Use dot notation to indicate the ROM contents. X $=$ AB$+$BC$\text{'}$D$+$A$\text{'}$B$\text{'}$ Y $=$ AB$+$BD Z $=$ A$+$B$+$C$+$D $2.$ Implement the functions from previous problem $($in question $1)$ using a PLA. You may use dot notation.