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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)
Given the function F(x,y,z) = xyztx,y2+xyz (a) List the truth table for F (b) Draw the logic diagram using the original Boolean expression (c) Simplify the expression (using any method you know) (d) Draw the logic diagram for the simplified expression.
Given the function f(x, y, z) = xy +xz write f (x, y, z) as a sum of min terms and a product of max terms.
(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)
Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 10z) k C is the line segment from (3, 0, -3) to (4, 4, 1) (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate [s vf. dr along the given curve C.
Use the gradient rules to find the gradient of the given function, f(x,y,z) = x+yz y+xz Choose the correct answer below. 1 O A. Vf(x,y,z) = -((1-z?)z(z2 - 1).y? - x?) (y + xz)? OB. Vf(x,y,z) = (z(1-z?)y(z? - 1),z2 + x2) (x + yz)? O c. Vf(x,y,z) = (y(1+z2),x(z? + 1).y? - z?) (x + yz)? OD. Vf(x,y,z) = -(y (1-2²), x(2² - 1), y² - x²) (y + xz)2
I Using K-Map minimize the function: f(x, y, z, w) = {(2, 4, 9, 15) + d(0, 1, 3, 6, 11,13) Do not use Boolean algebra. Use K-Maps.
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...
In the following diagram ifs,-1 and S 0 what will be the logic state at the output K? S2 Co Using DeMorgan's theorem, express the function F #ABC+ A'C' + A, B, with only OR and complement operators Using DeMorgan's theorem, express the function F = ABC + A,C, + A'B. with only AND and complement operators Convert the following expressions (AB +CB+ C'D) into sum-of-products (minterms) and product-of-sums (maxterms) Simplify the Boolean expression AB +ABC +ABCD +ABCDE+ABCDEF Which logic...
I just need help with the second one 4. Proof and simplification (16 points) a) Show that the following equation is valid using Boolean algebra axioms and theorems. Demonstrate your detailed steps. (8 points) BC+Ā B+AC = ABC+Ā b) Simplify the following logic equation: (8 points) F(X,Y,Z)=Y Z + XY + XZ + YZ