Section B$.$ The Sequence

$-$ The steps in a sequence are generated using a Pseudo$-$Random Number Generator

$($PRNG$).$ This PRNG is implemented using a Linear$-$Feedback Shift Register $($LFSR$)$

with the mask: MASK $=0$xE$2023$CAB. The initial state of the LFSR represents the

seed of the PRNG$,$ which must be initialised with your student number, encoded as a

$32-$bit hexadecimal literal.

Example:

Student number: n$12345678->$ STATE$\_$LFSR $=0$x$12345678$

Student number: n$5556667->$ STATE$\_$LFSR $=0$x$05556667$

$-$ Each step is derived from STATE$\_$LFSR through the following algorithm:

BIT $$ lsbit$($STATE$\_$LFSR$)$

STATE$\_$LFSR $$ STATE$\_$LFSR $>>1$

if $($BIT $=1)$

STATE$\_$LFSR $$ STATE$\_$LFSR xor MASK

STEP $$ STATE$\_$LFSR and $0$b$11$

$-$ The value of STEP specifies the tone to be played and the segments to be

illuminated. STEP $=0$ means that E$($high$)$ is to be played and segments EF are to be

illuminated on DIGIT $1.$ The user must then press pushbutton S$1$ to reproduce this

step. Similarly, STEP $=1$ means that C$$ is played and segments BC are illuminated

on DIGIT $1,$ and so on$.$

$-$ Upon successfully reproducing a sequence of steps, the sequence of steps in the next

turn will contain the same steps as in the current sequence, with an additional step

added to the end.

$-$ If the user fails to match Simon$$s sequence, the game will restart, and a new

sequence will be generated. This new sequence will commence from where the

current sequence ended.

Example:

Assume the seed $0$x$12345678$ where the user has reached turn $7$ with the

sequence $1341343$ and expected subsequent sequence $13413432.$ If the user

incorrectly enters a $1$ instead of a $3$ on the $5$th step, the game will end and restart

from the $8$th step. The sequence in the next turn will then have a length of one and

consist of the step $2.$

$-$ Upon system reset, the seed must be set back to its initial value, allowing the Simon

game to be replayed.