Question $2[20$ points$](15$ minutes$)$: A certain logic circuit has four inputs A$,$ B$,$ C$,$ and D$.$ The output X of the circuit is logic $1$ if two or more inputs are logic $1.$

a$-$ Write the truth table for this circuit

$(10$ points$)$

$\backslash$table$[[$A$,$B$,$C$,$D$,$X$],[0,0,0,0,],[0,0,0,1,],[0,0,1,0,],[0,0,1,1,],[0,1,0,0,],[0,1,0,1,],[0,1,1,0,],[0,1,1,1,],[1,0,0,0,],[1,0,0,1,],[1,0,1,0,],[1,0,1,1,],[1,1,0,0,],[1,1,0,1,],[1,1,1,0,],[1,1,1,1,]]$

b$-$ Implement the circuit using an $4$ to $16$ decoder or $3$ to $8$ decoders.

$(10$ points$)$

please solve it hand writting $($paper based$)$

please do your best $,$ i will rate you