In: Computer Science

Show the Karnaugh map representation of the function F() =, and
use it to find the minimum-cost **both Sum of Product
(SOP)** and **Product of Sum (POS)** forms for
the function F.

In many digital circuits and practical problems we need to find expression with minimum variables. We can minimize Boolean expressions of 3, 4 variables very easily using K-map without using any Boolean algebra theorems. K-map can take two forms Sum of Product (SOP) and Product of Sum (POS) according to the need of problem. K-map is table like representation but it gives more information than TRUTH TABLE. We fill grid of K-map with 0’s and 1’s then solve it by making groups.

**Steps to solve
expression using K-map-**

- Select K-map according to the number of variables.
- Identify minterms or maxterms as given in problem.
- For SOP put 1’s in blocks of K-map respective to the minterms (0’s elsewhere).
- For POS put 0’s in blocks of K-map respective to the maxterms(1’s elsewhere).
- Make rectangular groups containing total terms in power of two like 2,4,8 ..(except 1) and try to cover as many elements as you can in one group.
- From the groups made in step 5 find the product terms and sum them up for SOP form.

please give thumbs up if you like it

Use a Karnaugh map to find the minimum AND-OR expression for
x(a, b, c) with don’t-care conditions:
(c) Σ(1, 3) + d(0, 2, 4, 6)
(e) Σ(1, 7) + d(2, 4)

For each of the following functions, find all the minimum SOP
expressions using the Karnaugh map.
g(v,x,y,z,w)=
Σm(0,1,4,5,8,9,10,15,16,18,19,20,24,26,28,31)
(1 solution)

Find a function f such that F = ∇f and use it to compute R
C Fdr along curve C.
• F = <x, y>, C is part of the parabola y = x ^ 2 from (−1,
1) to (3, 9).
• F = <4xe ^ z, cos (y), 2x ^ 2e ^ z>, where C is
parameterized by r (t) = <t, t ^ 2, t ^ 4>, 0 ≤ t ≤ 1.

Consider the map f(x) =x^2+k .Find the values of k for
which the map f has
a) two fixed points
b) only one fixed point
c) no fixed points
For what values of k there will be an attracting fixed point of the
map?

Activity on Digestive System
Make a concept map that show the parts and function of
the digestive system and BRIEFLY discuss your concept map. upload
your work here in canvas.
Give at least 3 most common diseases related to
Digestive System and give the 4 aspects of disease(Etiology,
Pathogenesis, Morphologic Changes, and Clinical Manifestation) to
each diseases you give.
REPRODUCTIVE SYSTEM:
Make a concept map that show the parts and function of
the reproductive system and BRIEFLY discuss your concept...

Activity on Circulatory system:
"Make a concept map that show the parts and function
of the circulatory system and BRIEFLY discuss your concept map.
upload your work here in canvas.
Give at least 3 most common diseases related to heart,
blood , and blood vessels and give the 4 aspects of
disease(Etiology, Pathogenesis, Morphologic Changes, and Clinical
Manifestation) to each diseases you give."
Bond paper please. Thank you

Use Cauchy-Riemann equations to show that the complex function
f(z) = f(x + iy) = z(x + iy) is nowhere differentiable except at
the origin z = 0.6 points) 2. Use Cauchy's theorem to evaluate the
complex integral ekz -dz, k E R. Use this result to prove the
identity 0"ck cos θ sin(k sin θ)de = 0

discuss which is better: Boolean algebra or K-map?
What are the limitations of Karnaugh Maps? Explain with an
example.

(a) Consider the function f(x)=(ex −1)/x.
Use l’Hˆopital’s rule to show that lim f(x) = 1 when x
approaches 0
(b) Check this result empirically by writing a program to
compute f(x) for x = 10−k, k = 1,...,15. Do your results agree with
theoretical expectations? Explain why.
(c) Perform the experiment in part b again, this time using the
mathematically equivalent formulation, f(x)=(ex
−1)/log(ex), evaluated as indicated, with no
simplification. If this works any better, can you explain why?...

For the function f(x) = x(x+1) find the exact formula for f′(x).
Use only the definition of the derivative.

ADVERTISEMENT

ADVERTISEMENT

Latest Questions

- william brown is 30 years and wants to retire when he is 65. so far he...
- 1. List and elaborate on the reasons that there more singles today than ever before. 2....
- During December of the current year, Teletex Systems, Inc., a company based in Seattle, Washington, entered...
- Which FTP command allows you to retrieve a file from within an FTP session? 39. Company...
- When would a sequential colormap work well in a heatmap? Select an answer: when you want...
- Write a synopsis about the CPU in 300 words
- C++ program Dairy Farm decided to ship milk in containers in the form of cubes rather...

ADVERTISEMENT