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.
![GATE CSE 2024 Set 1 Digital Logic - Combinational Circuits Question 1 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lwue4qfr/69d79342-2f7f-483a-9024-215f90906dd0/51084e70-1f23-11ef-a538-9dce63b3efcd/file-6y3zli1lwue4qfs.png?format=png)
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 $$\overline A + \overline A \,.\,\overline C + A\,.\,\overline B \,.\,C$$ ?
![GATE CSE 2016 Set 1 Digital Logic - Combinational Circuits Question 7 English](https://gateclass.static.cdn.examgoal.net/De3LS1dPiPYqhdxbf/3EBIfXymY1bhN5dohn4LE5QbzBxu2/4TeJEcWjE3mXKuNprNNJav/uploadfile.jpg)
The minimal sum of products form of the output $$X$$ is
![GATE CSE 2014 Set 1 Digital Logic - Combinational Circuits Question 8 English](https://imagex.cdn.examgoal.net/IglwhDk4L7qtKS38b/2VJjNctKpxwu3XXRdjZXOQJjUytJO/MJC5ywucsIzJMMSA9Bt4Rj/uploadfile.jpg)
The minimal sum-of-products form of the Boolean expression for the output $$F$$ of the multiplexer is