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
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.
The following logic function is given as a sum of minterms F(W,X,Y,Z) = ∑W,X,Y,Z(2,7,10,13,14) + d(5,6,15) a) Draw the K-map for the given function F. b) What is the minimized SOP equation? c) Give all input pairs in the form of WXYZ where a transition between them would create a timing hazard. d) Draw the timing diagram showing the hazard for one of the cases. Assume ALL gate delays are equal. e) Provide the expression of an equivalent logic function...
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.
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z cos y, xz sin y, x cos y). a) Determine which vector field above is conservative. Justify. Foly = fjol so, <ea sin(J2), 20% cos(82), y acos (92)) Conservative. b) For the vector field that is conservative, find a function f such that F - Vf. Lxelsing2, zetos yea, yet cosy 2 c) Use the Fundamental Theorem of Line Integrals to find the work...
Construct a truth table then simplify the following functional expressions: a) F(x,y,z) = xyz + x(yz)' + x'(y+z) + (xyz)' b) F(x,y,z) = y(x'z + xz') + x(yz + yz')
Given the function F(x,y) = y'+(x+y) : a) Make a truth table for F. [4 marks] b) Express F as a sum of products. [3 marks] c) Simplify F, either algebraically or by an explanation based upon the truth table. [3 marks]
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.
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
1. Simplify the Boolean function (F(A, B, C, D) = ∏(3,4,6,7,11,12,13.14.15) a) Generate K-Map of F b) Obtain simplified sum-of-products form of F c) Obtain simplified product-of-sums form of F Note: you should show the final prime implicants you used
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.