Q$1(10$ points$)$: Design a combinational circuit with three inputs, x$,$ y and z$,$ and thethree outputs, A$,$ B$,$ and C$.$ when the binary input is $0,1,2,$ or $3,$ the binary output isone greater than the input. When the binary input is $4,5,6,$ or $7,$ the binary output isone less than the input.Q$2(5$ points$)$: Implement the Boolean function F$($A$,$B$,$C$)=$ AB $+$ A$\text{'}$C $+$ A'B'Using a single $4$x$1$ multiplexer.Q$3(5$ points$)$: Implement the same function in Q$2$ using the minimum number of $2$x$4$decoders with enable and a single NOR gate.Q$4(10$ points$)$: Implement the following function F$($A$,$B$,$C$,$D$)=(0,2,4,6,8,10)$usinga$.$ Mux $41$b$.$ Decoders $3-$to$-8$c$.$ AND$-$ORd. NAND$-$NANDQ$5(6$ points$)$: In the following function determine the Essential prime implicantF$($A$,$B$,$C$,$D$)=(0,2,5,7,6,8\mathrm{.}9,10,11,13,14,15)$Q$6(4$ points$)$: Explain the concept of odd parity generator?