$1\mathrm{.}2$ Circuits

Implement each of these circuits using Logisim and show that they work.

$1\mathrm{.}2\mathrm{.}1$ Quad $4-$to$-1$ multiplexor

Build a circuit to select among four $4-$line inputs. You may use a $2-$to$-4$ decoder from the Logisim components in your design.

$1\mathrm{.}2\mathrm{.}2$ Cascaded multiplexors

Build a single$-$line $8-$to$-1$ multiplexor using two $4-$to$-1$ multiplexors and one $2-$to$-1$ line multiplexor.

$1\mathrm{.}2\mathrm{.}3$ Boolean function using a single $4-$to$-1$ multiplexor

Implement the Boolean function

$F(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}m(1,3,4,11,12,13,14,15)$

with a $4-$to$-1$ multiplexor and external gates. Connect inputs A and $B$ to the selection lines. The input requirements for the four data lines will be a function of the variables $C$ and $D.$ The values of these variables are obtained by expressing $F$ as a function of $C$ and $D$ for each of the four cases when $AB=00,01,10,11.$ These functions must be implemented as external gates.

$1\mathrm{.}2\mathrm{.}4$ Boolean function using a dual $4-$to$-1$ multiplexor

Implement the Boolean function

$F(A,B,C,D)=m(0,1,2,3,7,8,13,15)$

using a dual $1-$to$-4$ data multiplexer.

a$.$ Enter the function into column F of the table.

b$.$ The four data lines will be a function of $C$ and $D$ for each of the four combinations of values of A and B$.$ Write the four functions here.

i$.,F(0,0,C,D)=$

ii$.F(0,1,C,D)=$

iii. $F(1,0,C,D)=$

iv$.F(1,1,C,D)=$

c$.$ Build and test the circuit.

$\backslash$table$[[,$A$,$B$,$C$,$D$,$F$,],[O$

$in$

$,0,0,0,0,,],[0,0,0,1,,],[0,0,1,0,,],[0,0,1,1,,],[,0,1,0,0,,],[0,1,0,1,,],[0,1,1,0,,],[0,1,1,1,,],[$

$,1,0,0,0,,],[1,0,0,1,,],[1,0,1,0,,],[1,0,1,1,,],[F$

$,1,1,0,0,,],[1,1,0,1,,],[1,1,1,0,,],[1,1,1,1,,]]$