A mission has a byte$-$oriented command and parameter architecture. Command

opcodes are all $16$ bits. Certain commands include strings of characters. The

following commands are among those defined for the mission:$$

FILE$\_$LOAD destination filepath$$

destination: $16$ bit unsigned int$$

filepath: null terminated string no greater than $60$ bytes$$

$$

START destination$$

destination: $16$ bit unsigned int$$

$$

STOP destination$$

$$

destination: $16$ bit unsigned int$$

Typical uplink sequences are placed in files and consist, on average, of $12$

FILE$\_$LOAD commands, $100$ START commands, $100$ STOP commands.$$

$$

This problem will compare the use of variable length parameters with fixed

length parameters. Recall that fixed length strings are padded with trailing

null characters. Remember that opcodes are not parameters.$$

$$

$$

a$)$ If $*$all command parameters$*$ have a variable length with a $1$ byte length field

preceding each parameter value, at what threshold of average filepath length

$($including a terminator$)$ do commands with parameters of variable length result

in smaller average sequence sizes than with fixed length commands? $($Answer in

bytes$).$ Note: we are only interested in the resulting file length, you can

ignore the CCSDS framing and packetization overhead.$$

$$

b$)$ If $*$only filepath command parameters$*$ have a variable length with a $1$ byte

length field preceding each parameter value, at what threshold of average

filepath length $($including a terminator$)$ do commands with parameters of variable

length result in smaller average sequence sizes than with fixed length commands?

$($Answer in bytes$).$ Note: we are only interested in the resulting file length,

you can ignore the CCSDS framing and packetization overhead.