_{3},S

_{2},S

_{1},S

_{0}) where S

_{3}is MSB and S

_{0}is LSB. Y is given in terms of minterms as $$Y\, = \,\sum m\left( {1,5,6,7,11,12,13,15} \right)$$ and its complements $$\overline Y \, = \,\sum m\left( {0,2,3,4,8,9,10,14} \right)$$.

(a) Enter the logical values in the given Karnaugh map [figure2(b)] for the output
Y.

(b) Write down the expression for Y in sum-of products from using minimum
number of terms.

(c) Draw the circuit for the digital logic boxes using four 2-input NAND gates
only for each of the boxes.

(a) Enter the logical values in the K-map in the format shown in figure 3(a). Derive
the minimal Boolean sum-of-products expression whose output is zero when a majority of the pumps fail.

(b) The above expression is implemented using logic gates, and point P is the
output of this circuit, as shown in figure 3(b). P is at 0 V when a majority of the pumps fails and is at 5 V otherwise. Design a circuit to drive the LED using this output. The current through the LED should be 10 mA and the voltage drop across it is 1V. Assume that P can source or sink 10 mA and a 5 V supply is available.