$[100$ points$]$

Nodes A and B are on a $10$ Mbps broadcast channel, and the propagation delay between the two

nodes is $500-$bit times. CSMA$/$CD protocol is used.

a$.$ What is the minimum frame size needed so that both A and $B$ detect collision if there is an

overlap in their transmissions regardless of when each starts transmission?

b$.$ Suppose A and B send frames at the same time, detect collision, and choose different values of

$K$ in the CSMA$/$CD algorithm; $K_A=0$ and $K_B=1.$ Assuming no other nodes are active, can the

retransmissions from A and B collide? Justify using a timing diagram.

$[$Hint: After backoff, a node must wait until the channel is idle and, then, the interframe gap for

an additional $96$ bit$-$times. Also, upon collision detection, a transmitting node stops its

transmission and sends a $48-$bit jamming signal. Analyze when the first bit of A$\text{'}$s retransmission

reaches B and when B starts its retransmission.$]$