V$.$ Consider a sensor network $7$ sensor nodes, $1$ Sink node, and the topology shown below. The

spanning tree shown is used to propagate messages from Nodes $2$ through $7$ to Node $1$ which

then transmits messages to the Sink. Note that link $5-6$ is not used in the spanning tree. Assume

all messages are $100$ bits long.

Energy is expended for different functions in each sensor node as indicated in the following table.

a$)$ During each sensing cycle, sensor nodes $1$ through $7$ each read their sensor$.$ Nodes $2$ through

$7$ then forward the value in a message up the spanning tree toward the Sink. Nodes $2,3,4,$

and $6$ also forward any received messages up the spanning tree toward the Sink. Node $1$

forwards its sensor value in message and all received messages to the Sink. Assume there is no

aggregation of data. For this scenario, how much energy is expended by Node $1$ during one

sensing cycle? Give your answer in units of $0,$

b$)$ During each sensing cycle, sensor nodes $1$ through $7$ each read their sensor$.$ Nodes $5$ and $7$

each forward their sensor values in a message up the spanning tree toward the Sink. Nodes $1,$

$2,3,4,$ and $6$ compute the maximum of their sensor value and all received values to create a

single result value. Nodes $2,3,4,$ and $6$ forward this value up the spanning tree toward the

Sink. Node $1$ sends this value to the Sink. For this scenario, how much energy is expended by

Node $1$ during one sensing cycle? Give your answer in units of $J$