The operating conditions (ON = 1, OFF = 0) of three pumps (x, y, z) are to be monitored.  implies that pump X is on. It is required that the indicator (LED) on the panel should glow when a majority of the pumps fail.

(a) Enter the logical values in the K-map in the format shown in figure. 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. 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 10mA and the voltage drop across it is 1V. Assume that P can source or sink 10mA and a 5V supply is available.