A traffic signal cycles from GREEN to YELLOW, YELLOW to RED and RED to GREEN. In each cycle, GREEN is turned on for 70 seconds, YELLOW is turned on for 5 seconds and the RED is turned on for 75 seconds. This traffic light has to be implemented using a finite state machine (FSM). The only input to this FSM is a clock of 5 second period. The minimum number of flip-flops required to implement this FSM is _______.

In the circuit shown below, a positive edge-triggered D Flip-Flop is used for sampling input data D_in using clock CK. The XOR gate outputs 3.3 volts for logic HIGH and 0 volts for logic LOW levels. The data bit and clock periods are equal and the value of $${{\Delta T} \over {{T_{CK}}}}$$ = 0.15, where the parameters $$\Delta T$$ and T_CK are shown in the figure. Assume that the Flip-Flop and the XOR gate are ideal.

If the probability of input data bit (D_in) transition in each clock period is 0.3, the average value (in volts, accurate to two decimal places) of the voltage at node X, is _______.

A 2 $$ \times $$ 2 ROM array is built with the help of diodes as shown in the circuit below. Here W₀ and W₁ are signals that select the word lines and B₀ and B₁ are signals that are output of the sense amps based on the stored data corresponding to the bit lines during the read operation.
During the read operation, the selected word line goes high and the other word line is in a high impedance state. As per the implementation shown in the circuit diagram above, what are the bits corresponding to D_ij (where i = 0 or 1 and j = 0 or 1) stored in the ROM?

Consider matrix $$A = \left[ {\matrix{ k & {2k} \cr {{k^2} - k} & {{k^2}} \cr } } \right]$$ and

vector $$X = \left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$.

The number of distinct real values of k for which the equation AX = 0 has infinitely many solutions is _______.