Design a logic circuit with a $4$ bits binary number that check the password if it is correct or not, the passwords $(0100,0010,0100,0101,0001,1001$and $1110).$

$1-$ 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.

$3-$ The passwords with odd value are master passwords, if the entered password is master activate the yellow$1$ led.

$4-$ If the entered password is not master, activate the yellow$2$ led.

The required:

$1-$ Write truth table.

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

$3-$ Draw the logic circuit of the system $($use only NOR gates$)$