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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...
Q3: 1. For the Boolean function shown below, answer the questions F(W,X,Y,Z) = 11 (6,8,9,10,11,12,13) use...
Q3: 1. For the Boolean function shown below, answer the questions F(W,X,Y,Z) = 11 (6,8,9,10,11,12,13) use K-MAP to: • Derive the BF as SOP. • Derive the BF as POS. • Find All prime implicants of the BF. • Determine the Essential prime implicant(s). 2. Let the BF change to have don't care condition as: F(W,X,Y,Z) = 1,3,7,11,15 + de E(0.2,5) Derive the BF as SOP and POS.
Use Boolean Algebra to simplify the following Boolean expressions to three (3) literals. Please write down...
Use Boolean Algebra to simplify the following Boolean expressions to three (3) literals. Please write down the intermediate steps. 1). F11(x,y,z) = x'yz+xyz +x'y'Z+xy'Z+ xy'z 2). F12(x,y,z) = (y'+xyz')' Question 2 [2 points) Obtain the function expression of F2 from the logic diagram. Question 3 [3 points) Obtain the truth table of the following function and rewrite the function in Canonical POS (Product of Maxterms) format: F3(a,b,c) = (a'+c)(a+b+c') +a'bc' Question 4 (2 points) Convert the following function to Canonical...
(06) Proof the following absorption theorem using the fundamental of Boolean algebra X+ XY= X (07)...
(06) Proof the following absorption theorem using the fundamental of Boolean algebra X+ XY= X (07) Use De Morgan's Theorem, to find the complement of the following function F(X, Y, Z) = XYZ + xyz (08) Obtain the truth table of the following function, then express it in sum-of-minterms and product-of-maxterms form F= XY+XZ (Q9) For the following abbreviated forms, find the corresponding canonical representations, (a) F(A, B, C) = (0,2,4,6) (b) F(X, Y, Z) = II (1,3,5,7)
Design a combinational circuit with three inputs, x , y, and z, and three outputs, A,...
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...
Consider the Boolean function F1 = X' · Z + X ' · Y · Z...
Consider the Boolean function F1 = X' · Z + X ' · Y · Z + X · Y ' + X · Y' · Z (a) Implement F1, in the form as given, using 2-input ANDs, 2-input ORs and NOT gates. How many gates did you use? (b) Simplify F1 using Boolean algebra identities. Show all the steps & the identities used at each step. (c) Implement the simplified form of F1 using 2-input ANDs, 2-input ORs and...
1. Find the Boolean expression of the truth table. Then simplify it and convert it into...
1. Find the Boolean expression of the truth table. Then simplify it and convert it into the least amount of logic gates possible. AB Output 100 011 101 2. Find the POS form of the Boolean expressions below. Find the truth table and logic minimization method of it. Show its gate level implementation, and show the same gate level implementation using only NAND gates. A(X,Y,Z)= m(0,2,4,6) B(X,Y,2)={m(0,4,5) 3. Create a J-k Flip Flop using a D-Flip Flop. Show its truth...
Name Use SOP, to find Boolean equation for the outputs X, Y, z Construct a logic...
Name Use SOP, to find Boolean equation for the outputs X, Y, z Construct a logic circuit using AND, OR, and Inverter (NOT) gates which implements the Boolean equations Substitute your logic circuits with NAND gates only, simplify the circuit. 1. 2. 3. Input Outputs A B C 0 0 0 0 0 0 0 0 011 0 0 0
QUESTION 1 [TOTAL MARKS:25] A manufacturing process has four sensors labelled W.X, Y. and Z. The...
QUESTION 1 [TOTAL MARKS:25] A manufacturing process has four sensors labelled W.X, Y. and Z. The system should sound an alarm if any of the following conditions arise: • W, X, Y, Z are not activated at the same time. • X, Y, and Z are not activated and W is activated at the same time. • Wand Y are not activated, and X and Z are activated at the same time. • W, X, and Z are not activated,...
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.
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).
Q2) Given the Boolean function F = xyz + xyz + xyz (a) List the truth...
Q2) Given the Boolean function F = xyz + xyz + xyz (a) List the truth table. (b) Draw the logic diagram of the original function using 2-input gates. (c) Simplify the function using K-Map. (d) Draw the logic diagram of the simplified function (using 2-input gates). (e) Draw the logic diagram of the simplified function using only 2-input NAND gates.
Q3: 1. For the Boolean function shown below, answer the questions F(W,X,Y,Z) = 11 (6,8,9,10,11,12,13) use K-MAP to: • Derive the BF as SOP. • Derive the BF as POS. • Find All prime implicants of the BF. • Determine the Essential prime implicant(s). 2. Let the BF change to have don't care condition as: F(W,X,Y,Z) = 1,3,7,11,15 + de E(0.2,5) Derive the BF as SOP and POS.
Use Boolean Algebra to simplify the following Boolean expressions to three (3) literals. Please write down the intermediate steps. 1). F11(x,y,z) = x'yz+xyz +x'y'Z+xy'Z+ xy'z 2). F12(x,y,z) = (y'+xyz')' Question 2 [2 points) Obtain the function expression of F2 from the logic diagram. Question 3 [3 points) Obtain the truth table of the following function and rewrite the function in Canonical POS (Product of Maxterms) format: F3(a,b,c) = (a'+c)(a+b+c') +a'bc' Question 4 (2 points) Convert the following function to Canonical...
(06) Proof the following absorption theorem using the fundamental of Boolean algebra X+ XY= X (07) Use De Morgan's Theorem, to find the complement of the following function F(X, Y, Z) = XYZ + xyz (08) Obtain the truth table of the following function, then express it in sum-of-minterms and product-of-maxterms form F= XY+XZ (Q9) For the following abbreviated forms, find the corresponding canonical representations, (a) F(A, B, C) = (0,2,4,6) (b) F(X, Y, Z) = II (1,3,5,7)
1. Find the Boolean expression of the truth table. Then simplify it and convert it into the least amount of logic gates possible. AB Output 100 011 101 2. Find the POS form of the Boolean expressions below. Find the truth table and logic minimization method of it. Show its gate level implementation, and show the same gate level implementation using only NAND gates. A(X,Y,Z)= m(0,2,4,6) B(X,Y,2)={m(0,4,5) 3. Create a J-k Flip Flop using a D-Flip Flop. Show its truth...
Name Use SOP, to find Boolean equation for the outputs X, Y, z Construct a logic circuit using AND, OR, and Inverter (NOT) gates which implements the Boolean equations Substitute your logic circuits with NAND gates only, simplify the circuit. 1. 2. 3. Input Outputs A B C 0 0 0 0 0 0 0 0 011 0 0 0
QUESTION 1 [TOTAL MARKS:25] A manufacturing process has four sensors labelled W.X, Y. and Z. The system should sound an alarm if any of the following conditions arise: • W, X, Y, Z are not activated at the same time. • X, Y, and Z are not activated and W is activated at the same time. • Wand Y are not activated, and X and Z are activated at the same time. • W, X, and Z are not activated,...
Q2) Given the Boolean function F = xyz + xyz + xyz (a) List the truth table. (b) Draw the logic diagram of the original function using 2-input gates. (c) Simplify the function using K-Map. (d) Draw the logic diagram of the simplified function (using 2-input gates). (e) Draw the logic diagram of the simplified function using only 2-input NAND gates.
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