Exercise $1$

We consider a circuit that selects between two inputs $(2$ to $1$ multiplexer$).$ It has an input x which is the selector between two other input wires i $0$ and il $.$ When $x=0,$ the output is the same as $i0,$ when $x=1,$ the output is the same as il$.$ See the below diagram:

Draw the truth table for that circuit, then get the expression of $f,$ simplify it and draw the circuit.

To make a bigger multiplexer $($such as $4$ to $1)$ we would need $4$ bits for the inputs and two for the selector, which would take too much time.

Instead let us continue with the example of the $2$ to $1$ multiplexer but this time it has two bits for the selection:

If the selection value is $0,$ it returns $i0$

If the selection value is $1,$ it returns il

If the selection value if $2,$ it returns ${10}^{**}il$

If the selection value if $3,$ it returns i$0+$il

Draw the truth table for that circuit using gray code, then get the expression of $f,$ simplify it and draw the circuit.

Exercise $1$

We consider a circuit that selects between two inputs $(2$ to $1$ multiplexer$).$ It has an input x which is the selector between two other input wires i $0$ and il $.$ When $x=0,$ the output is the same as $i0,$ when $x=1,$ the output is the same as il$.$ See the below diagram:

Draw the truth table for that circuit, then get the expression of $f,$ simplify it and draw the circuit.

To make a bigger multiplexer $($such as $4$ to $1)$ we would need $4$ bits for the inputs and two for the selector, which would take too much time.

Instead let us continue with the example of the $2$ to $1$ multiplexer but this time it has two bits for the selection:

If the selection value is $0,$ it returns $i0$

If the selection value is $1,$ it returns il

If the selection value if $2,$ it returns $i{0}^{**}i1$

If the selection value if $3,$ it returns $i0+$ il

Draw the truth table for that circuit using gray code, then get the expression of $f,$ simplify it and draw the circuit.