Q$1(10$ points$)$: Design a combinational circuit with three inputs, $x,y$ and $z,$ and the three outputs, A$,$ B$,$ and C$.$ when the binary input is $0,1,2,$ or $3,$ the binary output is one greater than the input. When the binary input is $4,5,6,$ or $7,$ the binary output is one less than the input.

Q$2(5$ points$)$: Implement the Boolean function $F(A,B,C)=AB+A^{\text{'}}C+A^{\text{'}}{B}^{\text{'}}$

Using a single $41$ multiplexer.

$Q3(5$ points$)$: Implement the same function in $Q2$ using the minimum number of $24$ decoders with enable and a single NOR gate.

Q$4(10$ points$)$: Implement the following function $F(A,B,C,D)=(0,2,4,6,8,10)$

using

a$.x{4}^{\text{'}}1$

b$.$ Decoders $3-$to$-8$

c$.$ AND$-$OR

d$.$ NAND$-$NAND

Q$5(6$ points$)$: In the following function determine the Essential prime implicant

$F(A,B,C,D)\frac{?}{b}=ar(2)(0,2,5,7,6,8*9,10,11,13,14,15)$

Q$6(4$ points$)$: Explain the concept of odd parity generator?