ECE 1315 Make-up Spring, 2009NAME: _________________________Exam II-makeup: 6 Exam Points – No Partial Credit1. (25 Points) Given the following function in four binary variables, with don’t-care states:F(W,X,Y,Z) = ∑m(2,5,8,10,15) + dc(0,4,7,12,13)a) Map the function on the K-Map and make minimal coverage of the Maxterms - CLEARLY label the map with your variables – Write the minimal POS expressionb) Map the function on the K-Map provided and make minimal coverage of the minterms - CLEARLY label the map with your variables - Write the minimal SOP expressionc) Algebraically manipulate either the SOP or POS equation above and IMPLEMENT using only a minimum number of 2:1 MUX gates. Assumeonly uncomplemented variables are available.Scott Norr Page 1 1/13/2019ECE 1315 Make-up Spring, 20092. (25 Points) Given two unsigned, decimal integers, A = 22 and B = 27, find the following:a) A and B as unsigned binary numbersb) A and B as positive 2’s complement numbersc) A and B as negative 2’s complement numbersd) Perform A MINUS B in 2’s complemente) Perform (–A) PLUS (–B) in 2’s complementScott Norr Page 2 1/13/2019ECE 1315 Make-up Spring, 20093. (15 Pts) Given a 3:8 Decoder that puts out minterms, and some NOR-2 gates, implement the function, F(A,B,C) = AB + AC’ + BC’ + A’B’C’4. (15 Pts) Given an 4:1 MUX only, implement the function, F(ABCD) = ∑m(0,1,5,7,13,15,8,9)Scott Norr Page 3 1/13/2019ECE 1315 Make-up Spring, 20095. (20 Pts) Create a CMOS logic circuit that implements:a) An OR-3 gateb) The function F(ABC) = AB + A’C + BCScott Norr Page 4