1. Using a Karnaugh map, find minimal SOP and POS expressions for f(w, x, y.) (1. 13, 15) + d (3, 5, 9) 2. Figure Q1(a) shows a combinational circuit with 3 inputs, A, B and C and I output, Z. Input A is the MSB whereas input C is the LSB. A B C Z Figure Q1(a) (i) Derive a Boolean expression for Z. (ii) Obtain the simplest Boolean expression for Z using Boolean theorem. (iii) Modify the circuit using only NOR gates with any number of inputs above 2. 3. A bulb in a staircase has two switches. One switch being at the ground floor (switch A) and the other one at the first floor (switch B). The bulb can be turned ON (F-1) and OFF (F=0) by any one of the switches irrespective of the state of the other switch. (i) Determine the expression, F that resembles the logic of switching of the bulb. (ii) Implement the expression found in part Q1(b)(i) using ONLY 2-input NAND gates 4. Design a circuit that counts the number of 1's present in 3 inputs A, B and C. Its output is a two-bit number XIX0, representing that count in binary. Assume active-HIGH logic. i. Write the truth table for this circuit. Find the minimized logic equations for outputs XI and XO; use a K-map if needed. ii. 5. Simplify the Boolean equation below using Karnaugh map. x=A+B+C+A+B+C+A+B+C+A+B+C+A+B+C 6. Given the Boolean expression z=(A+B).(B+D).(A+D).(C+D) (i) Draw the Karnaugh map (ii) Determine the minimum Sum of Product expression for Z. (iii) Draw the combinational logic circuit for Z. (iv) Based on circuit in part Q6(iii), modify the circuit using only NAND gates.