Task $1$: Checksum for Singapore car license plate number $[$Total: $70$ marks$]$

A Singapore car license plate, such as SHA$4022,$ E$43$A $,$ etc., consists of the following:

Prefix consisting of alphabets.

E$.$ SHA, SGJ$,$ QX$,$ FBB$,$ E

Numerical series from $1-9999,$ without leading zeros

E$.$g$.10,402,2222$

Checksum letter, one of these $19$ letters: $($A$,$ Z$,$ Y$,$ X$,$ U$,$ T$,$ S$,$ R$,$ P$,$ M$,$ L$,$ K$,$ J$,$ H$,$ G$,$ E$,$ D$,$ C$,$ B$)$

The checksum letter of a license plate validates if that license plate is valid or not.

In this task, write a program to calculate the checksum letter given a Singapore vehicle licence plate.

Here is the formula for calculating the checksum letter'

The last $2$ letters of the prefix are converted into digits, where $A=1,B=2,$dots, and $Z=26.$

If there is only $1$ letter, then convert that letter into digit, and add a digit $0$ to the front.

E$.SBS=2$ and $19,SH=19$ and $8,E=0$ and $5$

Add leading zeros to the numerical series to make it a $4$ digit figure.

E$.$e$.100010,4020402,22222222($no change$)$

Combine the prefox digits and the numerical series to form a series of six numbers.

E$.$ S$.$ SSS$10=>[2,19,0,0,1,0]$

Each individual numbers are then multiplied by the corresponding position of the six fixed numbers

$(9,4,5,4,3,2)$

E$.$g$.$ S$8$S$10->\{2,19,0,0,1,0]*(9,4,5,4,3,2]=[18,76,0,0,3,0]$

The multiplied numbers are then added up E$.$g$.(18,76,0,0,3,0)97$

Oivide the sum by $19$ and get the remainder.

E$.$g$.\frac{97}{19}=5$ remainder $2$

The remainder corresponds to one of the $19$ letters $($A$.$ Z$,$ Y$,$ X$,$ U$,$ T$,$ S$,$ R$,$ P$,$ M$,$ L$,$ K$,$ J$,$ H$,$ G$,$ E$,$ D$,$

C$.$ B$)$ where remainder $0$ corresponds to $\text{'}A\text{'},$ remainder $1$ corresponds to $Z\text{'}$ and so on$.$

E$.$g$.$ Checksum letter for remainder $2={}^{*}.$

Task $1$a $[10$ marks$]$

Write a function alphabet$\_$to$\_$digit $($c$).$ This function takes in an alphabet and converts it into its digit

representation where $A=1$ and $Z=26.$ Your function should be case insensitive, ie$.,$ to handle both upper

and lower case alphabets.

Note: You are strongly encouraged to use comments to describe your code where necessary.

Task $1$b $[10$ marks$]$

Write a function convert$\_$pref $1($prefix$).$ This function takes in a non$-$empty alphabet string called

prefix and returns a list of two integers, which are the converted digits of the last two alohabets in orefix.

For our question, we do not limit the number of alphabets in a prefix. i$.$e$.$ The prefix can be

$"$SBSBCSBSDBSZBS$",$ but still only the last two characters are taken for conversion.

$.$ i$.$e$.\text{'}$SBSBCDZBS$\text{'}$ should return $2,19$ and $\text{'}$E$\text{'}$ should return $0,5$

Note: You are strongly encouraged to ure comments to describe your code where necessary.

Task $1$c $[10$ marks$]$

Write a function convert$\_$num$\_$series $($num$\_$series$).$ This function takes in a non$-$empty string of at

most four digits $($a number from the numerical series$)$ and returns a list of integers representing exactly $4$ Note: You are strongly encouraged to use comments to describe vour code where necessary.

Task $1$c $[10$ marks$]$

Write a function convert$\_$num$\_$series $($num$\_$series$).$ This function takes in a non$-$empty string of at

most four digits $($a number from the numerical series$)$ and returns a list of integers representing exactly $4$

digits.

i$.$e$.\text{'}10\text{'}$ should return $0,0,1,0$ and $\text{'}2222\text{'}$ should return $2,2,2,2$

Note: You are strongly encouraged to use comments to describe vour code where necessary.

Task $1$d $[10$ marks$]$

Write a function multiply$\_$and$\_$add$($series$).$ This function takes in a list of six integers and multiplies

each integer with the corresponding number in $9,4,5,4,3,2$ to obtain a new list of six integers; it then

returns the sum of these integers.

Note: You are strongly encouraged to use comments to describe vour code where necessary.

Task $1e[10$ marks$]$

Task $1$e: Write the function remainder$\_$to$\_$checksum$\_$letter$($remainder$)$ that takes in an integer

checksum remainder $($ranging from $0$ to $18)$ obtained in step $6$ of the formula and returns the

corresponding checksum letter $($in uppercase$).$

i$.$e$.0$ should return $\text{'}$A$\text{'}$ and $18$ should return $\text{'}$B$\text{'}.$

Note: You are strongly encouraged to use comments to describe your code where necessary. Task $1f$

Complete the function checksum$\_$calculator $($plate$)$ by putting everything together and returning the

checksum letter in uppercase given a license plate. Reminder: $1.$ Your program should be able to handle

lowercase inputs. $2.$ The prefix