(i) As Sum of minterms:
(It is already the sum of minterms form)
where min terms are xy and yz
(ii) The product of max terms
(This is the product of max terms)
where max terms are y and x+z
5. Given f(X,Y,Z)- XZ(XY+XY'), a) Express f as a minterm expansion b) Express f as a minterm expansion c) Express f as a max term expansion d) Express f as a max term expansion. Use m/M notation.
I. a) (4 points) For a given function F(x, y, z) = xz + (y + z)(x + z) Draw the logic circuit diagram of the function: b) Using Boolean Algebra to simply the above function c) Use Demorgan's Theorem to find out the complement of the above function F(x,y,z)xz+ + 2)(x +z)
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.
Given the function : F = x + ( (yz)’(x’ + y’+ z’) )’ A) Write the truth table of F. B) Draw the K-map for F. C) Using the K-map, write the fully simplified Sum-Of-Products expression for F. D) Write the fully simplified product-of-sums expression for F
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
5. Let F(x, y, z) = (yz, xz, xy) and define Cr,h = {(x, y, z) : x2 + y2 = p2, z = h}. 1 Show that for any r > 0 and h ER, Sony F. dx = 0
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)
5. Let F(x, y, z) = (yz, xz, xy) and define 2 Crin = {(x,y,z) : x2 + y2 = r2, 2 = h} Show that for any r > 0 and h ER, le F. dx = 0 Crih
Consider the function given below, F = (X+Y)(X + XY)2 + X(Y + 2) + XY + XYZ (a) Simplify the given function to its Sum of Products. (b) Draw gate-level schematic of simplified F function. (c) Realize this function with CMOS transistors and draw transistor-level schematic.
What is the domain and range of the function f(x, y, z) = xz + e^y?