Question

a) Represent the following logic function F(w, x, y, z) on a 4 variable K-map F(w, x, y, z) = Σm(6, 7, 9, 10, 13) + dc(4, 5, 11, 15)

b)Write down the list of the function’s prime implicants (PI) and the essential prime implicant(s) (EPI), if any

c)Find a minimum expression in a sum-of-products form of the logic function F(w, x, y, z).

Answer #1

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9. Find a sum-of-products expression for F’ for the function
F(W, X, Y, Z) = X + YZ(W + X’)

Find the truth table (function table), SOM, POM, and
simplify the expression using K Map approach of the following Sigma
notation expression: (10 points) f(w,x d y,z)= sum
m(0,3,9,10,14,15)

Convert the following expression to SOP form
F= (W+X) Y*Z) (W+YXX*Y*Z)

Find the maximum and minimum values of the function f(x, y, z) =
x^2 + y^2 + z^2 subject to the constraints x + y + z = 4 and z =
x^2 + y^2 .

Assume that you are asked to design a logic circuit with the
following specifications, using
K-map. The circuit has two inputs X and Y and three outputs O0,
O1 and O2. This circuit
operates as follows: (1) the output (O0) will be high when
X<Y only, (2) the output (O1)
will be high when X>Y only, and (3) the output (O2) will be
high when X=Y only.
a. (3 points) Create the truth table for this logic circuit.
b. (3...

A function f”R n × R m → R is bilinear if for all x, y ∈ R n and
all w, z ∈ R m, and all a ∈ R: • f(x + ay, z) = f(x, z) + af(y, z)
• f(x, w + az) = f(x, w) + af(x, z) (a) Prove that if f is
bilinear, then (0.1) lim (h,k)→(0,0) |f(h, k)| |(h, k)| = 0. (b)
Prove that Df(a, b) · (h, k) = f(a,...

(Lagrange Multipliers with Three Variables) Find the global
minimum value of f(x,y,z)=(x^2/4)+y^2 +(z^2/9) subject to x - y + z
= 8. Now sketch level surfaces f(x,y,z) = k for k = 0; 1; 4 and the
plane x-y +z = 8 on the same set of axes to help you explain why
the point you found corresponds to a minimum value and why there
will be no maximum value.

4. Consider the function z = f(x, y) = x^(2) + 4y^(2)
(a) Describe the contour corresponding to z = 1.
(b) Write down the equation of the curve obtained as the
intersection of the graph of z and the plane x = 1.
(c) Write down the equation of the curve obtained as the
intersection of the graph of z and the plane y = 1.
(d) Write down the point of intersection of the curves in (b)
and...

Find the value of the directional
derivative of the function w = f ( x , y , z ) = 2 x y + 3 y z
- 4 x z
in the direction of the vector v =
< 1 , -1 , 1 > at the point P ( 1 , 1 , 1 ) .

Simplify the following Boolean functions, using K-maps. Find all
the prime implicants, and determine which are essential:
(a) F (w, x, y, z) = ? (1, 4, 5, 6, 12, 14, 15)
(b) F (A, B, C, D) = ? (2, 3, 6, 7, 12, 13, 14)
(c) F (w, x, y, z) = ? (1, 3, 4, 5, 6, 7, 9, 11, 13, 15)

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