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For the function: F(W,X,Y,Z) = "\\prod" M(0,3,4,6,7,9,11,15):
a) identify the essential prime implicants
b) Write the minimal sum
with the aid of an example, explain how even and odd parity work and give an example application where they may be useful.
Explain and illustrate why a NAND gate is considered a universal gate
implement a two-level OR-AND logic circuit given the truth table of 3 inputs below:
A B C F
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 0
Given that F(X,Y,Z) = "\\bar{X}" + Z(X+"\\bar{Y}" ) use algebraic manipulation to derive the canonical POS expression for F
Do the following in given bases
a) B6F16-3748. give answer in base 2
b) 01000101BCD - 70910 in 8-bit 2's complement
Perform following conversion
a) 0111011102 to gray code
b) 10110111 gray code to binary
c) 56610 to 84-2-1 code
d) -8910 to 8-bit sign magnitide and 1's complement
. State the converse, contrapositive, and inverse of each of these conditional statements. A positive integer is a prime only if it has no divisors other than 1 and itself.
- Let X1, X2 , and X3 be independent standard normal random variable. If we defined Y1=X2, Y2=X1+X2/2 and Y3=X1+ X2 +X3/3.Then find then joint pdf of Y1, Y2, and Y3 using the Jacobian method?
Phenomena such as waiting times and equipment failure times are
commonly modelled by exponentially decreasing probability density functions. Find the exact form of such a function.
1. The time to complete the production of certain product for two machines produced by two different
well−known companies (company A and B) were observed to be completely different. The time machine from company A takes to complete the production (in hours) is X~Exp(2) and the time machine from company B takes to produce the product (in hours) is Y~Unif(0, 1). If the performances of the two machines is assumed to independent, what is the distribution of Z = X + Y, the total time they take to complete the production of the product? Hint: use the convolution method.
#340153 on Dec 2023