Question

G1 = (A’+C’+D) (B’+A) (A+C’+D’)

G2 = (ABC’) + (A’BC) + (ABD)

G3 = (A+C) (A+D) (A’+B+0)

G4 = (G1) (A+C)

G5 = (G1) (G2)

G6 = (G1)+(G2)

Determine the simplest product-of-sums (POS) expressions for G1 and G2.

Determine the simplest sum-of-products (SOP) expressions for G3 and G4.

Find the maxterm list forms of G1 and G2 using the product-of-sums expressions.

Find the minterm list forms of G3 and G4 using the sum-of-products expression.

Find the minterm list forms of G1 and G2 using the maxterm list forms of G1 and G2.

Find the minterm list forms of G5 and G6 using the minterm list forms of G1 and G2.

Answer #1

follow the page number order at top corner

For the expression
g(t) = g1(t) + g2(t) + g3(t) = Acos(2πft + θA)
where
g1(t) = 35cos(2πft − 15o) g2(t) = 25sin(2πft + 30o)
g3(t) = 15cos(2πft)
and f = 4000 Hz,
a.) Find a phasor expression in polar form for g1(t) ↔ ˜ G1.
Express the angle in degrees. (use a calculator to evaluate any
trigonometric expressions)
b.) Find a phasor expression in polar form for g2(t) ↔ ˜ G2.
Express the angle in degrees. (use a calculator...

Consider the sequence g0 = 1,
g1 = 1, g2 = 21,
g3 = 41, g4 = 461,
g5 = 1281, g6 = 10501,...
whose linear generator is gn+2 =
gn+1 + 20gn, that is, 20(!)
pairs of baby rabbit offspring.
As we did for the Fibonacci numbers, please derive a closed
form expression for gn.
Consider the sequence hn =
(–1)n gn:
1,–1,21,–41,461,–1281,10501,... Please give a second order
homogeneous linear recurrence with constant coefficients for
hn and prove that...

Simplify the following expression written in sum-of-products
(SOP) form and present it in product-of-sums (POS) form: ¯AB C D +
¯AB C ¯ D + A ¯ B ¯ C ¯ D + A ¯ B ¯C D

(a)
For the following quadratic forms gi(x) write down the
associated symmetric matrix Ai such that gi(x) = xT Aix.
g1(x1, x2) = x21 − 2x1x2 + 4x2
g2(x1, x2) = 4x21 − 6x1x2 + x2
g3(x1, x2, x3) = 3x21 + 3x2 + 5x23 + 2x1x2 − 2x1x3 − 2x2x3
g4(x1, x2, x3) = −3x21 − x2 + 8x2x3 − 16x23
(b) Determine the definiteness of g1(x) and g3(x) using the
method of eigenvalues.
(c) Determine the definiteness of...

When does transcription occur?
A. mitosis
B. meiosis
C. G1
D. G2
E. S

f(a,b,c) =
Xm(0,1,5)
Use boolean algebra to simplify both of the above expressions to
determine the minimal sum-of-products and the minimal
product-of-sums representation for the above function.

Logic Circuit
Problem #3
Given the following logic function: F(a,b,c,d) = ?
m(0,3,7,9,11,13,15)+?d(4,6,8) use a Karnaugh Map to, a) Find a
minimal SOP expression Answer: F(a,b,c,d) = b) Find a minimal POS
expression
Answer: F(a,b,c,d) =
Problem #4
Implement the function F(a,b,c,d) given in problem #3 using two
3-to-8 decoders, both active low enabled and active low output.
F(a,b,c,d) = ? m(0,3,7,9,11,13,15)+?d(4,6,8)
Answer:
Problem #5
Implement the function in the previous problem: F(a,b,c,d) = ?
m(0,3,7,9,11,13,15)+?d(4,6,8), using a single 4...

Find the simpliest SOP expression using boolean algebra.
F(A,B,C,D) = A’B’CD + A’BCD’ + A’BCD + AB’C’D’ + AB’C’D +
ABC’D’

Let A = (−5,3,5), B = (−10,0,2), C = (−5,0,−3), and D =
(0,3,0).
a) Find the area of the parallelogram determined by these four
points.
b) The area of the triangle ABC
c) The area of the triangle ABD.

Write the canonical SOP expression for the function
F(a, b, c, d)=∑m(2, 3, 9, 10, 11, 13) and
then simplify using algebraic manipulation.

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