COSC/ELEN 2448: Introduction to Digital System Design Homework #3 Due Date: February 22nd, 2019 Exercise 1: Plot each of the following functions on a manual K-map. Circle each adjacent group of 1s to identify each expression. Write the reduced functions in SOP form. a) F(A,B,C,D)-Zn1(2,3,47,11)+ md(5,15) b) F(A, B, C,D)-2m(0,2,5,7,8,10,13)+2md (4,6,14) NOTE: md are don't care terms. Exercise 2: Design a circuit using the 1s of the following function. F(W,X, Y,z)-m(0,2,5,7,8,10) + md (12,13) If possible, reduce the function. Draw the circuit for the function using just NAND gates. Exercise 3: Design a circuit using the 1s of the following function. F(X,Y,Z) m(0,1,4) If possible, reduce the function. Draw the circuit for the function using just NOR gates. (Hint: You may use a K-map to derive the simplified Boolean function as the Product-of-Sum of Max-terms, and then draw the circuit using the basic fundamental logic gates) Exercise 4: Implement the circuit that would eliminate all logic 1 hazards that can result for the circuit with the following Boolean function F(A, B, C) = > m(1,3,4,5) Show the K-maps and the equations for the minimum Boolean function and the logic hazard-free Boolean function. Exercise 5: Design a circuit for the following function using a 3-to-8 decoder with active low outputs. F(X, Y, Z) = m(0,1,5,6,7) Use an appropriate gate to provide the smallest possible fan-in to implement the function. February 15, 2019 COSC/ELEN 2448: Introduction to Digital System Design Homework n3 Exercise6 Design the circuit for the system with the function F (A, B, C) and using ONLY the following components: - m( 1,2,4,7) a) A single 8-to-1 Multiplexer b) A single 3-to-8 decoder with active high outputs, and a NOR gate. Exercise 7: Detemine the waveform of the output F for the combinational logic circuit with the following Boolean equation and the inputs A, B, and C Exercise 8: Determine the minimized Boolean equation for the function performed by the following circuit. 5V MUX +5V MUX C o February 15, 2019