question 2.1
question 2.2:
2. Boolean Logic 2.1. Demonstrate the following identity by means of algebraic manipulations. !(x+y)z+x!y y (x+z)...
please answers all of them! 1. Simplify, using algebraic manipulations, the following Boolean expressions to a mini- mum number of terms and factors. (a) XYZ + XY + XYZ (b) XYZ + XZ 2. Find the complement of the following expression: (a) XY + XY 3. Using DeMorgan's Theorem, express the following function .... (a) F= XY+XY + ÝZ ... with only OR and complement operations. 4. Propose and solve your own logic simplification problem using logic theorems 5. Simplify...
Multiplexer Example Implement the following Boolean function using a 4x1 Mux; F(x,y,z) = Σ (1,2,6,7) Decoder Example Implement the following functions for a full adder using decoder; S(x,y,z) = Σ (1,2,4,7) C(x,y,z) = Σ (3,5,6,7) Implement the following Boolean function; F(x,y,z) = Σ (0,2,3,7): Using; 1. Two 2x4 decoders and logic gates 2. One 4x1 multiplexer Decoder . Draw the truth table for the function to be implemented. . Pick the terms for output. . Derive appropriate logic to combine terms. . Use two 2x4 decoders to make one3x8 decoder. . Pay attention to fact...
c & e only please 2.1 + Demonstrate the validity of the following identities by means of truth tables: (a) De Morgan's theorem for three variables: (x + y + z)' = x'y'z' and (xyz)' = x y + z' (b) The distributive law: x + yz = (x + y)(x + z) (c) The distributive law: x(y + z) = xy + xz (e) Associative law: x(yz) = (xy)z
Boolean Logic A. Show the truth table for this expression: X AND (Y XOR X) B. Show the truth table for this expression: Y OR (Y AND NOT X) C. Show the truth table for this expression: X NOR (Y NAND X) D. Draw a digital logic circuit for the expression used in 3A. E. Draw a digital logic circuit for the expression used in 3B. F. Draw a digital logic circuit for the expression used in 3C.
Question 2: Combinational Logic (15 points) Implement the following Boolean function Z(A,B,C,D) = {(1,2,5,7,8,10,11,13,15) 2.1 (5 points) Write the truth table for Z. 2.2 (5 points) Implement Z using a single 16:1 multiplexer. Make sure that you mark all inputs and outputs clearly. 2.3 (5 points) Implement Z using an 8:1 multiplexer and all necessary gates. Make sure that you mark all inputs and outputs clearly.
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.
5. Apply Boolean algebra theorems to minimize the following expression. x(y + xy) + xy(x + yy) 6. Consider the following digital circuit diagram. Write the corresponding logic expression for f and the truth table. D A $(91, 02, ) f(x1, X2, X3)
PRELIMINARY WORK 2: FUNCTIONS OF LOGIC GATES F (xyz) Figure 2.1-3-input-NAND Gate design by using just 2-input-NAND Gates Figure 2.2- Design of function F-xy+x'z, by using just 2-input-NAND Gates Simulate the logic circuits that are given in figure 2.1 and figure 2.2. Simulations can be done in Proteus, P-Spice or any simulation program that you want to use. You can take screenshot of your design for print out. Please fill the table 2.1 according to your simulation results. Experiment results...
Design a combinational circuit with three inputs, x , y, and z, and three outputs, A, B , and C . When the binary input is 0, 1, 2, or 3, the binary output is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is two less than the input. 1) Truth table 2) Logic circuit 3) Boolean function of A using minterms ( use Boolean algebra) 4) Boolean function of...
7) Construct the truth table for the function F(X,Y,Z) = Y’Z+ X Z’ 8) Draw the logic circuit for the function F(X,Y,Z) = Y’Z+ X Z’