partb Problem 2 [15 points] Consider again the function F(x, y, z, w) from problem 1....
problem3
Prof. Tassos Dimitriou Homework 3 Deadline: Monday, April 1, 2019, IN CLASS Problem 3 [10 points a) (5 points) Construct a circuit that takes as input a 3-bit number X - X2XiXo and increments it by one. Le. if the input is 101 the output should be 110. Use only half adders. b) Construct a circuit that takes as input a 3-bit number X-xx,xo and decrements it by one. 1. (5 points) Show the truth table of the circuit....
Q31 For the figure shown below W is an input, (X, Y and Z) are connected to (S2, S and So), find the Boolean function F (W, X, Y, Z) in SOP and implement it use: 1. Multiplexer: One-piece (4 to 1) and external gates (W, X are selectors). 2. Decoder: Five (2 to 4) with AND gate. 0 1 8 to 1 MUX Do D, F OP D, S S S 35 Marks] X Y Z
Q31 For the...
6. Given F(x,y,z) = x'yz + xz (20 points) 1) Express F as a sum of minterms using algebraic manipulation. (5 points) F(x, y, z)= (x'y + 2) Draw the truth table for F (5 points) 3) Implement the original function F using 2-input gates. (5 points) 4) Simplify Fusing algebraic mplify F using algebraic manipulation. (5 points)
Q2: 1. Proof this Boolean expression. Use Boolean Algebra (X+Y). (Z+W).(X'+Y+W) = Y.Z+X.W+Y.W 2. For this BF F(X,,Z)=((XYZ)(X +Z))(X+Y) • Design the digital circuit Derive the Boolean Function of X, Y, Z. Simplify the Function Derive the truth table before and after simplification. Derive the BF F(X,Y,Z) as Maxterms (POS) and miterms (SOP). Implement the F(X,Y,Z) after simplification using NAND gates only. Implement the F(X,Y,Z) after simplification using OR NOR gates only.
Implement the Boolean function F(w,x,y,z) = Σm(3, 4, 5, 1 1, 12, 13, 14, 15) using a minimum number of NAND gates only. Write the minimal logic expression (no need to draw the circuit).
part c
Problem 3 [10 points a) (5 points) Construct a circuit that takes as input a 3-bit number X-XXXo and increments it by one. L.e. if the input is 101 the output should be 110. Use only half adders. b) Construct a circuit that takes as input a 3-bit number X-XXxo and decrements it by one 1. (5 points) Show the truth table of the circuit. Then use a decoder and additional gates to implement it. So Ys Y2...
Implement the function F (x,y,z)= (not x)(not z)+ xy using a. One 4-to-1 multiplexer and any additional inverters. Show your truth-table and justify your choice of select inputs. b. One 2-to-1 multiplexer and the minimal number of gates. Show the truth table used to derive your circuit.
3) (10 points) Implement F(A, B, C) = m(0,1,4,7) using an 2-to-1 MUX (use the symbol) and any other basic logic gates necessary (AND, OR, or NOT gates). Show the truth table and minimize any combinational logic (other than the MUX) in sum-of-products form. Use the left most input(s) for the MUX select input(s) in your schematic.
Given the function below, F(w,x,y,z)= x’z+w’z’+w’y a) draw a logic diagram for an implementation which uses only five two-input NOR gates. b) Implement the function of parts a using only four two-input NAND gates. Draw the logic diagram. USE K-MAP TO SOLVE.
Question #6 6 points Implement the function from the truth table below (X, Y, Z are inputs. F is the output) using a) An 8:1 multiplexer b) A 4:1 multiplexer and one inverter c) A 2:1 multiplexer and two other logic gates Y z F 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 -