Given the two Boolean function n sum of minterms

$F_1(A,B,C,D)=(0,1,4,5,8,9,10,12,13)$

$F_2(A,B,C,D)=(3,5,7,8,10,11,13,15)$

a$.$ Simplify the two functions by means of K$-$maps.

b$.$ Obtain a composite logic diagram with four inputs and two outp

c$.$ Implement two functions together using a minimum number of NAND Gates

d$.$ Connect the circuit and check its operation

Design a combinational circuit with four inputs, $A,B,C,$ and D $,$ and one output, F$.$ F is to be equal to $1$ when $A=1$ provided that $B=0,$ or when $B=1$ provided that either C or D is also equal to $1.$ Otherwise, the output is to be equal to $0.$

a$.$ Obtain the truth table of the circuit

b$.$ Simplify the output function.

c$.$ Draw the logic diagram of the circuit using NAND Gates with a minimum number of gates

d$.$ Construct the circuit and test it for proper operation by verifying the conditions stated above.