Consider the digital circuit shown below with two input lines A and B, two select lines S 0 and S 1 , and an output line Y . The blocks Q and M represent active high $2: 4$ decoder and 4-to-1 multiplexer, respectively. Out of 16 possible input combinations, the number of combinations that produce $\mathrm{Y}=1$ is $\_\_\_\_$ . (answer in integer)

Note: One input combination is an instance of [A B S1 S0].

Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1 and X2 are inputs of M1. X3 and X4 are inputs of M2. A, B, and C are select lines of M1, M2, and M3, respectively.

For an instance of inputs X1=1, X2=1, X3=0, and X4=0, the number of combinations of A, B, C that give the output Y=1 is ______________

A Boolean digital circuit is composed using two 4-input multiplexers (M1 and M2) and one 2-input multiplexer (M3) as shown in the figure. X0-X7 are the inputs of the multiplexers M1 and M2 and could be connected to either 0 or 1. The select lines of the multiplexers are connected to Boolean variables A, B and C as shown.

Which one of the following set of values of (X0, X1, X2, X3, X4, X5, X6, X7) will realise the Boolean function $$\overline A + \overline A \,.\,\overline C + A\,.\,\overline B \,.\,C$$ ?

Consider the two cascaded $$2$$-to-$$1$$ multiplexers as shown in the figure.

The minimal sum of products form of the output $$X$$ is