Q$3.(10$ Marks$)$

The perceptron could be used to perform numerous logic functions, such as AND, OR$,$

COMPLEMENT and NAND function, whose truth tables are tabulated as follows

respectively.

AND

OR

COMPLEMENT

NAND

a$).$ Demonstrate the implementation of the logic functions AND, OR$,$ COMPLEMENT

and NAND with selection of weights by off$-$line calculations.

$(3$ Marks$)$

b$).$ Demonstrate the implementation of the logic functions AND, OR$,$ COMPLEMENT

and NAND with selection of weights by learning procedure. Suppose initial weights

are chosen randomly and learning rate $$ is $1.$ Plot out the trajectories of the weights

for each case. Compare the results with those obtained in $($a$).$ Try other learning rates,

and report your observations with different learning rates.

$(4$ Marks$)$

c$).$ What would happen if the perceptron is applied to implement the EXCLUSIVE OR

function with selection of weights by learning procedure? Suppose initial weight is

chosen randomly and learning rate $$ is $1\mathrm{.}0.$ Do the computer experiment and explain

your finding.

$(3$ Marks$)$