Homework: commanding$$

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Set up all solutions mathematically.$$

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Show calculations symbolically before substituting numbers to make$$

partial credit possible.$$

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Mark the final answer with an arrow:$$

e$.$g$.$

$12\mathrm{.}7738$ bps $<--$

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Problem $1$

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A mission has a maximum uplink rate of $500$ bps$,$ and an emergency uplink rate of$$

$5$ bps$.$ There are $200$ spacecraft command opcodes, including $3$ critical commands$$

interpreted by hardware. The leading bit of these hardware commands is required$$

to be $1$ in order to be identified by the legacy transponder. Each command frame$$

to the spacecraft has $16$ bits of header information and $8$ bits of trailer$$

information. The data payload may contain any number of bits. There are no$$

internal packets within the frame: the command is the only data in the payload$$

of the frame.$$

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When in safe mode, the spacecraft accepts $5$ bps uplink. Switching to the$$

highest uplink rate requires sending $5$ commands individually and receiving

confirmation from the spacecraft before sending the next one. Each is shown as

an opcode$$

followed by zero or more parameters:$$

SOLAR$\_$ARRAY $14$ ENABLE$$

UPL$\_$ANTENNA MEDIUM$\_$GAIN ENABLE$$

ACS$\_$MODE EARTH$\_$TRACK$$

UPL$\_$RATE $500$

UPL$\_$REINIT$$

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The commands given have the following formats and parameter value ranges:$$

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SOLAR$\_$ARRAY$$

$1$: array number $(1.\mathrm{.}32)$

$2$: ENABLE, DISABLE$$

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UPL$\_$ANTENNA$$

$1$: LOW$\_$GAIN, MEDIUM$\_$GAIN, HIGH$\_$GAIN$$

$2$: ENABLE, DISABLE$$

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ACS$\_$MODE$$

$1$: EARTH$\_$TRACK, SUN$\_$TRACK$$

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UPL$\_$RATE$$

$1$: unsigned integer value $5.\mathrm{.}500$

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UPL$\_$REINIT$$

$($no parameters$)$

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a$\mathrm{.}1)$ For a minimum length bit$-$oriented command system, how many uplink bits are$$

necessary to bring the spacecraft out of low rate uplink mode?$$

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Hint: use base $2$ binary multiples to figure out number of bits needed for each

parameter.$$

e$.$g: $0.\mathrm{.}256$ is $257$ values$$

$1$ bit provides $2$ values $(2^1)$

$2$ bits provides $4$ values $(2^2)$

$3$ bits provides $8$ values $(2^3)$

$...$

$8$ bits provides $256$ values $(2^8)$

$9$ bits provides $512$ values $(2^9)$

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$256<257<512,$ so $512$ values allows $257$ representations, therefore $9$ bits

needed$$

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a$\mathrm{.}2)$ How long will this transmission take?$$

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b$\mathrm{.}1)$ For a minimum length byte$-$oriented command system where opcodes and$$

parameters must be a multiple of $8$ bits in length, how many uplink bits are$$

necessary to bring the spacecraft out of low rate uplink mode?$$

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b$\mathrm{.}2)$ How long will this transmission take?$$

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c$)$ The flight software group is coding in C and does not wish to perform the

overhead required for bit shifting. The group wants to use byte$-$oriented

software commands: each command opcode and parameter would have a length some

multiple of $8$ bits. Should they be allowed to do so$?$ Justify your answer