For the logic circuit shown in Figure, the required input condition (A, B, C) to make the output (X)=1.

For the logic circuit shown in the figure, the simplified Boolean expression for the output Y is

The operating conditions (ON = 1, OFF = 0) of three pumps (x,y,z) are to be monitored. x = 1 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 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.

A sequential circuit using D flip-flop and logic gates is shown in the figure, where X and Y are the inputs and Z is the output. The circuit is