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Analyze the logic network in Fig. and simplify it by using properties of Boolean expressions.
Determine the basis functions in terms of which Sum-of products expressions are defined for functions of n = 3 variables.
Write the Sum-of-products expression for the truth-table of a 2-bit comparator (f1, f2, f3).
Consider the function f(x1, x2, x3) given by the set of decimals indices corresponding to the 1-minterms {2, 4, 7}.
Derive the Positive-polarity Reed-Muller expression for functions of n = 3 variables by the recursive application of the positive Davio expansion rule.
Determine PPRM-expression for the function f(x1, x2, x3) which takes the value 0 for the assignments of input variables.
Determine the maximum number of terminals that can use the channel.
An alternative derivation for the throughput in a pure ALOHA system may be obtained from the relation G = S+ A.
Determine the variance s2 in the number of arrivals in the interval T.
The probability that another packet will arrive within 1 s; within 100 ms.
Consider a pure ALOHA system that is operating with a throughput S = 0.1 and packets are generated with a Poisson arrival rate ?.
Consider a CSMA/CD system in which the transmission rate on the bus is 10 Mbits/s.
Now suppose that P1 = 10P2 and that the signal from user 2 is decoded first. Determine the sum capacity of the two-user system.
Consider the set A of all divisors of the number 100 and the binary relation ? over A defined by x?y if and only if x divides y.
Consider the set A of all divisors of the number 8 and the binary relation ? over A defined by x?y if and only if x divides y
Define the complete disjunctive normal form for the logic complement f ?of f.
Determine the complete disjunctive and conjunctive forms of the function f(x1, x2, x3, x4) .
Prove the equivalence of these functions also by using the complete conjunctive normal form.
Determine the decision variables for the separate ML decoding of the symbols.
Determine the probability of error for the detector with input metrics given by Equation for BPSK modulation and a Rayleigh fading channel.
For a Rayleigh fading channel and BPSK modulation, determine the performance of a MISO (2, 1) system.
Sketch the block diagram configuration of the transmitter and the receiver, illustrating the modulation and demodulation operations.
Determine the covariance matrix of the noise at the output of the detector.
Find the optimal power allocation and channel capacity when H is known at the transmitter and the receiver.
Determine and compare the outage probabilities for the two systems. Which MISO system has a lower outage probability for the same SNR?