Design a logic circuit with a $4$ bits binary number that check the password if it is correct or not, the passwords $(0100,0010,0100,0101).$

$1-$ If the entered $4$ bits equal one of the passwords, displayed the letter $1$ in a $7-$segment display and activate green led.

$2-$ If the entered $4$ bits does not equal one of the passwords, displayed the letter $0$ in a $7-$segment display and activate red led.

The required:

$1-$ Write truth table.

$2-$ Determine simplified Boolean expression for the output.

$3-$ Connect the logic circuit using simulation program.

$4-$ Explain each step

$5-$ Write a research about combinational circuits.