Copmplete the task bellow using only multiplexers

Task

Please design one combinational circuit according to the following requirements:

Combinational Circuits $$ Password Locker

Input:

The circuit takes in four $4-$bit binary numbers independently.

Output:

The circuit outputs $0$ in all cases expect when the $4$ binary numbers are the last $4$ digits of your student ID in order.

For example, if your student ID is $123456789,$ then the circuit should output $0$ unless $6,7,8,9$ are given as the first, second, third and forth input number. If the order is changed, such as $7689,$ the circuit should still output $0.$

Requirements:

$1.$ Convert the last $4$ digits of your student ID to $4-$bit binary numbers. $(5\%)$

$2.$ Write down the truth table of the circuit. $(25\%)$

a$.$ If you break the overall circuit into smaller circuit, write down the truth table of each part.

$3.$ Draw k$-$map of the truth table. $(25\%)$

a$.$ Same as item $2,$ write down the k$-$map of each part.

$4.$ Write down the output equation in Sum$-$of$-$Products format. $(15\%)$

a$.$ Same as item $2,$ write down the Sum$-$of$-$Products format of each part.

$5.$ Implement your schematic circuit with Logisim. $(30\%)$

a$.$ You must submit the project file along with your handwritten$/$printed work out process.