Consider a gate control system that requires a combination of access card validation,

biometric scan validation, time$-$based access restrictions, and an emergency override

feature. The gate should open under the following conditions:

If both the access card and biometric scan are valid, regardless of the time.

If the access card is valid and it is within the specified time range for special

access.

In case of an emergency, the gate should open irrespective of access card,

biometric scan, or time conditions.

Boolean Variables:

A: Access Card Valid $(1$ for valid, $0$ for invalid$)$

B: Biometric Scan Valid $(1$ for valid, $0$ for invalid$)$

T: Time within Special Access Range $(1$ for within range, $0$ for outside range$)$

E: Emergency Override $(1$ for emergency, $0$ for normal operation$)$

O: Gate Open Signal $(1$ for open, $0$ for closed$)$

Based on the above description, you are required to do the following:

a$)$ Construct a truth table representing the system described above, and find the Boolean

expression describing each output

b$)$ Using Boolean algebra, reduce the Boolean expressions obtained to their minimum form

c$)$ Using logic gates, create a circuit which achieves the described behavior of the system