Consider a local area network $($LAN$)$ with multiple stations connected to the same bus using the Carrier Sense Multiple Access with Collision Detection $($CSMA$/$CD$)$ protocol for medium access control.

Assume that each station has a packet to transmit and follows the CSMA$/$CD protocol to access the medium. The first station to sense the medium finds it idle and starts transmitting its packet. The second station also senses the medium as idle and starts transmitting its packet, but halfway through the transmission, it detects a collision with the first station's packet.

After detecting the collision, the second station follows the backoff and retransmission procedure specified by the CSMA$/$CD protocol. Assume that the backoff algorithm uses binary exponential backoff with a maximum number of retries of $10$ and that the slot time is $512$ bit times.

$($a$)(10$ points$)$ What is the minimum number of slots the second station must wait before attempting to retransmit its packet after detecting the collision? Show your calculations.

$($b$)(10$ points$)$ Assume that after the first retransmission, the second station detects another collision with a third station. What is the value of the backoff timer for the second retransmission? Show your calculations.

$($c$)(10$ points$)$ Compare and contrast the CSMA$/$CA protocol used in wireless LANs with the CSMA$/$CD protocol used in wired LANs. What are the main differences between these two protocols and what are the advantages and disadvantages of each?