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Lab Session: Strings, Structures and Bit Manipulation
Exercise 1: Strings are Arrays of Characters
Background
You may recall that in Lab 1, we defined strings variables as:
char animal[100] = "cat";
As you may guess now, we were actually creating an array of characters.
You may have noticed that we can print out a string without needing to specify the total
number of characters:
char animal[100] = "ferocious kitten";
printf("The %s sleeps!", animal);
The above code will print out "The ferocious kitten sleeps", even though the
char array animal contains 100 chars. This is because the final character is a special
ascii-null character: '\0' (added automatically by the compiler in this case)
Technical details
Dealing with strings:
#include
#include // extra include!
int main() {
char animal[100] = "ferocious kitten";
// length of the string
int length = strlen(animal);
int i;
for (i=0; i printf("%c", animal[i]);
}
printf("\n");
getchar();
return 0;
}
We can also copy strings.
#include
#include
int main () {
char orig[100]= "Cats are awesome";
char next[100];
UoG-UESTC 2020 Page 2 of 9
// 99 is the maximum number of chars
strncpy(next,orig,99);
printf("%s\n", next);
getchar();
return 0;
}
Your task...
The Coleman-Liau Index test[1] is an easily-computable estimation of the difficulty of
reading some text. It gives an approximate "grade level" (in US school system: grade 1 is
for students 5-6 years old, and the numbers increase linearly until grade 12).
𝐶𝐿𝐼 = 5.89 (
characters
words ) − 29.5 (
sentences
words ) − 15.8
In the above formula, "character" means "letter" -- for the purposes of that formula, spaces
and periods do not count as characters.
[1] Coleman, M.; and Liau, T. L. (1975); A computer readability formula designed
for machine scoring, Journal of Applied Psychology, Vol. 60, pp. 283-284.
Original journal paper (campus access only)
Write a program that calculates the Coleman-Liau Index of some text.
• Perform the actual calculation in a function which accepts char text[] as input
and returns the Coleman-Liau grade level.
• If the calculated grade is less than 1, set it to 1 instead of returning a lower
number.
• You may assume that the text:
o begins with a word
o ends with a period
o contains no numbers or non-letters
o there is one space between words, and one space after a period (other
than the final period).
o each sentence ends with a period; no exclaimation marks or question
marks are used.
(hint: what is the relationship between the number of periods, number of spaces,
and the words+sentences in the text?)
(another hint: how can you count the number of periods and spaces in the text?)
• Test it with the following three exerpts. For these definitions, you may ignore the
code style requirement that lines should be less than 80 characters long. When
you cut&paste this into your .c file, you might need to ensure that it all goes onto
one line.
UoG-UESTC 2020 Page 3 of 9
1. char text[100] = "I like cats. Cats like me. Miao miao
miao. Dogs are bad. Bad dogs bad.";
(words of wisdom)
(hint: the above fragment has 70 characters, 51 letters, 15 words, 14
spaces, 5 periods, 5 sentences, and a calculated CLI of -5.6, which we
change to be grade 1.)
2. char text[500] = "Tomorrow, and tomorrow, and
tomorrow, Creeps in this petty pace from day to day,
To the last syllable of recorded time; And all our
yesterdays have lighted fools The way to dusty death.
Out, out, brief candle. Life's but a walking shadow,
a poor player That struts and frets his hour upon the
stage And then is heard no more. It is a tale Told by
an idiot, full of sound and fury Signifying nothing."
(Macbeth: Act 5, Scene 5, lines 19-28)
3. char text[1000] = "Existing computer programs that
measure readability are based largely upon subroutines
which estimate number of syllables, usually by
counting vowels. The shortcoming in estimating
syllables is that it necessitates keypunching the
prose into the computer. There is no need to estimate
syllables since word length in letters is a better
predictor of readability than word length in
syllables. Therefore, a new readability formula was
computed that has for its predictors letters per
hundred words and sentences per hundred words. Both
predictors can be counted by an optical scanning
device, and thus the formula makes it economically
feasible for an organization such as the US Office of
Education to calibrate the readability of all
textbooks for the public school system."
(abstract of Coleman-Liau journal paper.)
(optional: research and implement the Automated Readibility Index (ARI). Compare
those results with the Coleman-Liau results.)
Note: Show your work to a demonstrator/GTA.
Exercise 2: Combining variables with struct
Background
You may have noticed that functions can only return one variable. But what if want to
return more information than we can hold in one variable? The answer is to pack multiple
variables together into a single structure.
This creates a new type of variable which contains a number of fields. In this section's
example, we create a new type of variable called struct SquareData. We can declare
UoG-UESTC 2020 Page 4 of 9
this just like other variables -- instead of writing int or float, we write
struct SquareData.
After we have declared a variable of this type with:
struct SquareData mySquare;
we can access its fields with mySquare.side, mySquare.area or any other field
name after the period.
Returning a struct is a modern addition to the language. It was not supported in the
original C standard in 1972, but was added in the ANSI C standard (also sometimes known
as "C89" or "C90"). Some very old compilers might not support ANSI C. We will see
another way to return multiple values in a few weeks.
Technical details
Structure:
#include
struct SquareData {
float area;
float perimeter;
int side;
};
struct SquareData calcSquare(int x) {
//define variable of data type structure
struct SquareData mySquare;
mySquare.side = x;
mySquare.perimeter = 4*x;
mySquare.area = x*x;
// we need to return this to main()
return mySquare;
}
void printStuff(struct SquareData mySquare) {
// this is not useful here, but it works
float areaBAD = mySquare.area;
printf("The square's sides are ");
printf("%i units long, ", mySquare.side);
printf("and thus has \nan area of ");
printf("%f units, and ", areaBAD);
printf("a perimeter of ");
printf("%f units.\n", mySquare.perimeter);
}
int main() {
UoG-UESTC 2020 Page 5 of 9
struct SquareData square;
square = calcSquare(2);
printStuff(square);
getchar();
return 0;
}
The syntax of a struct is a bit confusing. Make sure that you follow the example
carefully when you use them. Be particularly careful about the final semicolon “;“after
the struct definition's final ”}”, and about adding struct in front of the structure's
name.
Here's another example of struct:
#include
struct TimeData {
int total_minutes;
int hours;
int minutes;
};
struct TimeData calcTime(int day_minutes) {
struct TimeData time;
time.total_minutes = day_minutes;
time.hours = day_minutes / 60;
time.minutes = day_minutes % 60;
return time;
}
void printTime(struct TimeData myTime) {
printf("It has been ");
printf("%i", myTime.total_minutes);
printf(" minutes since midnight.\n");
printf("The time is therefore ");
printf("%02i:", myTime.hours);
printf("%02i ", myTime.minutes);
printf("o'clock.\n");
}
int main() {
struct TimeData time;
time = calcTime(123);
printTime(time);
time = calcTime(1234);
printTime(time);
getchar();
return 0;
UoG-UESTC 2020 Page 6 of 9
}
Your task...
Vending machines use simple programs to calculate the amount of change to return. For
a machine, the coins are dispensed mechanically. In our program, we will output the
numbers to the screen, looking something like this:
Customer gave 10 pence, item(s) cost 7 pence.
Give customer:
£2 £1 50 20 10 5 2 1
0 0 0 0 0 0 1 1
Customer gave 70 pence, item(s) cost 56 pence.
Give customer:
£2 £1 50 20 10 5 2 1
0 0 0 0 1 0 2 0
Customer gave 200 pence, item(s) cost 124 pence.
Give customer:
£2 £1 50 20 10 5 2 1
0 0 1 1 0 1 0 1
Customer gave 2000 pence, item(s) cost 1232 pence.
Give customer:
£2 £1 50 20 10 5 2 1
3 1 1 0 1 1 1 1
Write a program that calculates the amount of coins to return.
Before you begin, figure out the math on paper. Show your formula(s) to a lab
demonstrator before you start programming.
• Your int main() loop must be this:
int main() {
struct Change coins;
coins = getChange(7, 10);
printChange(coins);
coins = getChange(56, 70);
printChange(coins);
coins = getChange(124, 200);
printChange(coins);
coins = getChange(1232, 2000);
printChange(coins);
getchar();
return 0;
}
Remember that C is case-sensitive. As far as the computer is concerned, UPPERCASE
letters are completely different from lower-case letters!
• You must write the getChange(...) and printChange(...) functions, and
the definition of struct Change. The first function must do all the math; the
second function must do all the printf(...). Use the struct Change to pass
information between these functions.
UoG-UESTC 2020 Page 7 of 9
• Britain has the following coins: 1 pence, 2 pence, 5 pence, 10 pence, 20 pence, 50
pence, 1 pound (100 pence), and 2 pounds (200 pence). Your machine should not
dispense any bills.
• You may assume that your vending machine has an infinite amount of coins, but
you should always dispense the largest coins first.
• You do not need to print the pound £ symbol. You may output 200 instead of £2.
• Your program should use int for all variables, and keep track of the number of
pence instead of pounds.
You should never keep track of money with float.
Can you guess why?
(optional: try using float (storing pounds, not pence) to program your vending machine.
Can you make it give accurate results?)
Note: Show your work to a demonstrator/GTA.
Exercise 3: Bit manipulation
Background
As engineers, you will (or should at least!) have more interest in bitwise manipulation
than most other programmers. Writing software that controls lights, reacts to flipped
switches, and generally anything that interacts closely with hardware will require bitwise
operations. The main concepts here are flags and bitmasks (commonly known as "masks).
A flag is a particular bit with a special meaning. For example, when representing negative
numbers, the 8th bit could be thought of a flag which indicated whether the remainder of
the bits should be interpreted as a positive or negative number.
A bitmask is a way of accessing a particular bit (generally, but not always, a flag). The
bitmask is a number which has 0 in all bits we don't care about, and a 1 for the bit(s) that
we want to examine. By anding the bitmask with the original number, we can "extract"
the bit(s) -- if that bit was 0, then the new number will be completely zero; if the bit was 1,
then the new number will be non-zero.
The same operation is done in reverse to set a flag -- by oring a bitmask and the data
variable, we can set a flag to be true. Setting a flag can be done by anding the variable with
the noted bitmask.
Technical details
Various bitwise operations:
#include
int main() {
char x = 0x10; // number in hex
char y = 63;
printf("char is a one-byte number. ");
UoG-UESTC 2020 Page 8 of 9
printf("Printing it with %%c will treat ");
printf("it as\nan ASCII value, but we ");
printf("can also print it as a number: ");
printf("x=%i y=%i.\n", x, y);
printf("Some operations: ");
printf("%i\t%i\n", ~x, ~y);
printf("%i\t%i\t%i\n", x&y, x|y, x^y);
getchar();
return 0;
}
Toggling individual bits:
#include
#include // extra includes!
#include
float getRand() {
return rand() / (RAND_MAX+1.0);
}
int main() {
srand( time(NULL) ); // init random
char x = 0;
char bit, bitmask;
int i;
// Building a bitwise random number
for (i=0; i<8; i++) {
// set bit as 1 or 0?
if (getRand() > 0.5) {
bit = 1;
} else {
bit = 0;
}
// get bit ready
bitmask = bit << i;
// or them together
x = x | bitmask;
printf("After round %i, ",i);
printf("bit is %i, and ", bit);
printf("x is %i.\n", x);
}
getchar();
return 0;
}
Your task...
UoG-UESTC 2020 Page 9 of 9
Dougie Dog has invented an "encryption" technique to keep secrets from the Ferocious
Kittens. Fortunately, cats are extremely intelligent, and have cracked the simple code:
1. Letters are grouped into pairs. Add a space to the end of the string if necessary to
give it an even number of characters (here "character" means char.
2. Make an int from each pair by sticking the bits from the first letter in front of the
bits from the second letter. You may assume that we are using 8-bit ASCII.
3. XOR the result with 31337.
Here's two examples of encryption: "cats" and "kittens".
1. Pairs: "ca ts"
"ki tt en s_" (_ represents a space)
2. into ints: 25441 29811
27497 29812 25966 29472
3. XOR with 31337: 6408 3610
4352 3613 7943 2377
Decryption is performed with the same steps, but in reverse order.
• The Ferocious Kittens have intercepted two secret messages from Dougie Dog:
15643 6913 6916 23040 2377 6985 6408 3657 5638 3084 2119
15910 23079 13629 23101 10300 10557 23073 13092 23369
• Write a program that decrypts them.
(hint: this will be a lot easier if you begin by writing a program to encrypt values -
- you can check each step with "cats" and "kittens" to make sure you understand
the process!)
• You must use a function to split a large integer into two separate letters. This
function may not print anything to the screen.
(hint: how can a function return two values?)
Note: Show your work to a demonstrator/GTA.
Lab Session: Strings, Structures and Bit Manipulation
Exercise 1: Strings are Arrays of Characters
Background
You may recall that in Lab 1, we defined strings variables as:
char animal[100] = "cat";
As you may guess now, we were actually creating an array of characters.
You may have noticed that we can print out a string without needing to specify the total
number of characters:
char animal[100] = "ferocious kitten";
printf("The %s sleeps!", animal);
The above code will print out "The ferocious kitten sleeps", even though the
char array animal contains 100 chars. This is because the final character is a special
ascii-null character: '\0' (added automatically by the compiler in this case)
Technical details
Dealing with strings:
#include
#include
int main() {
char animal[100] = "ferocious kitten";
// length of the string
int length = strlen(animal);
int i;
for (i=0; i
}
printf("\n");
getchar();
return 0;
}
We can also copy strings.
#include
#include
int main () {
char orig[100]= "Cats are awesome";
char next[100];
UoG-UESTC 2020 Page 2 of 9
// 99 is the maximum number of chars
strncpy(next,orig,99);
printf("%s\n", next);
getchar();
return 0;
}
Your task...
The Coleman-Liau Index test[1] is an easily-computable estimation of the difficulty of
reading some text. It gives an approximate "grade level" (in US school system: grade 1 is
for students 5-6 years old, and the numbers increase linearly until grade 12).
𝐶𝐿𝐼 = 5.89 (
characters
words ) − 29.5 (
sentences
words ) − 15.8
In the above formula, "character" means "letter" -- for the purposes of that formula, spaces
and periods do not count as characters.
[1] Coleman, M.; and Liau, T. L. (1975); A computer readability formula designed
for machine scoring, Journal of Applied Psychology, Vol. 60, pp. 283-284.
Original journal paper (campus access only)
Write a program that calculates the Coleman-Liau Index of some text.
• Perform the actual calculation in a function which accepts char text[] as input
and returns the Coleman-Liau grade level.
• If the calculated grade is less than 1, set it to 1 instead of returning a lower
number.
• You may assume that the text:
o begins with a word
o ends with a period
o contains no numbers or non-letters
o there is one space between words, and one space after a period (other
than the final period).
o each sentence ends with a period; no exclaimation marks or question
marks are used.
(hint: what is the relationship between the number of periods, number of spaces,
and the words+sentences in the text?)
(another hint: how can you count the number of periods and spaces in the text?)
• Test it with the following three exerpts. For these definitions, you may ignore the
code style requirement that lines should be less than 80 characters long. When
you cut&paste this into your .c file, you might need to ensure that it all goes onto
one line.
UoG-UESTC 2020 Page 3 of 9
1. char text[100] = "I like cats. Cats like me. Miao miao
miao. Dogs are bad. Bad dogs bad.";
(words of wisdom)
(hint: the above fragment has 70 characters, 51 letters, 15 words, 14
spaces, 5 periods, 5 sentences, and a calculated CLI of -5.6, which we
change to be grade 1.)
2. char text[500] = "Tomorrow, and tomorrow, and
tomorrow, Creeps in this petty pace from day to day,
To the last syllable of recorded time; And all our
yesterdays have lighted fools The way to dusty death.
Out, out, brief candle. Life's but a walking shadow,
a poor player That struts and frets his hour upon the
stage And then is heard no more. It is a tale Told by
an idiot, full of sound and fury Signifying nothing."
(Macbeth: Act 5, Scene 5, lines 19-28)
3. char text[1000] = "Existing computer programs that
measure readability are based largely upon subroutines
which estimate number of syllables, usually by
counting vowels. The shortcoming in estimating
syllables is that it necessitates keypunching the
prose into the computer. There is no need to estimate
syllables since word length in letters is a better
predictor of readability than word length in
syllables. Therefore, a new readability formula was
computed that has for its predictors letters per
hundred words and sentences per hundred words. Both
predictors can be counted by an optical scanning
device, and thus the formula makes it economically
feasible for an organization such as the US Office of
Education to calibrate the readability of all
textbooks for the public school system."
(abstract of Coleman-Liau journal paper.)
(optional: research and implement the Automated Readibility Index (ARI). Compare
those results with the Coleman-Liau results.)
Note: Show your work to a demonstrator/GTA.
Exercise 2: Combining variables with struct
Background
You may have noticed that functions can only return one variable. But what if want to
return more information than we can hold in one variable? The answer is to pack multiple
variables together into a single structure.
This creates a new type of variable which contains a number of fields. In this section's
example, we create a new type of variable called struct SquareData. We can declare
UoG-UESTC 2020 Page 4 of 9
this just like other variables -- instead of writing int or float, we write
struct SquareData.
After we have declared a variable of this type with:
struct SquareData mySquare;
we can access its fields with mySquare.side, mySquare.area or any other field
name after the period.
Returning a struct is a modern addition to the language. It was not supported in the
original C standard in 1972, but was added in the ANSI C standard (also sometimes known
as "C89" or "C90"). Some very old compilers might not support ANSI C. We will see
another way to return multiple values in a few weeks.
Technical details
Structure:
#include
struct SquareData {
float area;
float perimeter;
int side;
};
struct SquareData calcSquare(int x) {
//define variable of data type structure
struct SquareData mySquare;
mySquare.side = x;
mySquare.perimeter = 4*x;
mySquare.area = x*x;
// we need to return this to main()
return mySquare;
}
void printStuff(struct SquareData mySquare) {
// this is not useful here, but it works
float areaBAD = mySquare.area;
printf("The square's sides are ");
printf("%i units long, ", mySquare.side);
printf("and thus has \nan area of ");
printf("%f units, and ", areaBAD);
printf("a perimeter of ");
printf("%f units.\n", mySquare.perimeter);
}
int main() {
UoG-UESTC 2020 Page 5 of 9
struct SquareData square;
square = calcSquare(2);
printStuff(square);
getchar();
return 0;
}
The syntax of a struct is a bit confusing. Make sure that you follow the example
carefully when you use them. Be particularly careful about the final semicolon “;“after
the struct definition's final ”}”, and about adding struct in front of the structure's
name.
Here's another example of struct:
#include
struct TimeData {
int total_minutes;
int hours;
int minutes;
};
struct TimeData calcTime(int day_minutes) {
struct TimeData time;
time.total_minutes = day_minutes;
time.hours = day_minutes / 60;
time.minutes = day_minutes % 60;
return time;
}
void printTime(struct TimeData myTime) {
printf("It has been ");
printf("%i", myTime.total_minutes);
printf(" minutes since midnight.\n");
printf("The time is therefore ");
printf("%02i:", myTime.hours);
printf("%02i ", myTime.minutes);
printf("o'clock.\n");
}
int main() {
struct TimeData time;
time = calcTime(123);
printTime(time);
time = calcTime(1234);
printTime(time);
getchar();
return 0;
UoG-UESTC 2020 Page 6 of 9
}
Your task...
Vending machines use simple programs to calculate the amount of change to return. For
a machine, the coins are dispensed mechanically. In our program, we will output the
numbers to the screen, looking something like this:
Customer gave 10 pence, item(s) cost 7 pence.
Give customer:
£2 £1 50 20 10 5 2 1
0 0 0 0 0 0 1 1
Customer gave 70 pence, item(s) cost 56 pence.
Give customer:
£2 £1 50 20 10 5 2 1
0 0 0 0 1 0 2 0
Customer gave 200 pence, item(s) cost 124 pence.
Give customer:
£2 £1 50 20 10 5 2 1
0 0 1 1 0 1 0 1
Customer gave 2000 pence, item(s) cost 1232 pence.
Give customer:
£2 £1 50 20 10 5 2 1
3 1 1 0 1 1 1 1
Write a program that calculates the amount of coins to return.
Before you begin, figure out the math on paper. Show your formula(s) to a lab
demonstrator before you start programming.
• Your int main() loop must be this:
int main() {
struct Change coins;
coins = getChange(7, 10);
printChange(coins);
coins = getChange(56, 70);
printChange(coins);
coins = getChange(124, 200);
printChange(coins);
coins = getChange(1232, 2000);
printChange(coins);
getchar();
return 0;
}
Remember that C is case-sensitive. As far as the computer is concerned, UPPERCASE
letters are completely different from lower-case letters!
• You must write the getChange(...) and printChange(...) functions, and
the definition of struct Change. The first function must do all the math; the
second function must do all the printf(...). Use the struct Change to pass
information between these functions.
UoG-UESTC 2020 Page 7 of 9
• Britain has the following coins: 1 pence, 2 pence, 5 pence, 10 pence, 20 pence, 50
pence, 1 pound (100 pence), and 2 pounds (200 pence). Your machine should not
dispense any bills.
• You may assume that your vending machine has an infinite amount of coins, but
you should always dispense the largest coins first.
• You do not need to print the pound £ symbol. You may output 200 instead of £2.
• Your program should use int for all variables, and keep track of the number of
pence instead of pounds.
You should never keep track of money with float.
Can you guess why?
(optional: try using float (storing pounds, not pence) to program your vending machine.
Can you make it give accurate results?)
Note: Show your work to a demonstrator/GTA.
Exercise 3: Bit manipulation
Background
As engineers, you will (or should at least!) have more interest in bitwise manipulation
than most other programmers. Writing software that controls lights, reacts to flipped
switches, and generally anything that interacts closely with hardware will require bitwise
operations. The main concepts here are flags and bitmasks (commonly known as "masks).
A flag is a particular bit with a special meaning. For example, when representing negative
numbers, the 8th bit could be thought of a flag which indicated whether the remainder of
the bits should be interpreted as a positive or negative number.
A bitmask is a way of accessing a particular bit (generally, but not always, a flag). The
bitmask is a number which has 0 in all bits we don't care about, and a 1 for the bit(s) that
we want to examine. By anding the bitmask with the original number, we can "extract"
the bit(s) -- if that bit was 0, then the new number will be completely zero; if the bit was 1,
then the new number will be non-zero.
The same operation is done in reverse to set a flag -- by oring a bitmask and the data
variable, we can set a flag to be true. Setting a flag can be done by anding the variable with
the noted bitmask.
Technical details
Various bitwise operations:
#include
int main() {
char x = 0x10; // number in hex
char y = 63;
printf("char is a one-byte number. ");
UoG-UESTC 2020 Page 8 of 9
printf("Printing it with %%c will treat ");
printf("it as\nan ASCII value, but we ");
printf("can also print it as a number: ");
printf("x=%i y=%i.\n", x, y);
printf("Some operations: ");
printf("%i\t%i\n", ~x, ~y);
printf("%i\t%i\t%i\n", x&y, x|y, x^y);
getchar();
return 0;
}
Toggling individual bits:
#include
#include
#include
float getRand() {
return rand() / (RAND_MAX+1.0);
}
int main() {
srand( time(NULL) ); // init random
char x = 0;
char bit, bitmask;
int i;
// Building a bitwise random number
for (i=0; i<8; i++) {
// set bit as 1 or 0?
if (getRand() > 0.5) {
bit = 1;
} else {
bit = 0;
}
// get bit ready
bitmask = bit << i;
// or them together
x = x | bitmask;
printf("After round %i, ",i);
printf("bit is %i, and ", bit);
printf("x is %i.\n", x);
}
getchar();
return 0;
}
Your task...
UoG-UESTC 2020 Page 9 of 9
Dougie Dog has invented an "encryption" technique to keep secrets from the Ferocious
Kittens. Fortunately, cats are extremely intelligent, and have cracked the simple code:
1. Letters are grouped into pairs. Add a space to the end of the string if necessary to
give it an even number of characters (here "character" means char.
2. Make an int from each pair by sticking the bits from the first letter in front of the
bits from the second letter. You may assume that we are using 8-bit ASCII.
3. XOR the result with 31337.
Here's two examples of encryption: "cats" and "kittens".
1. Pairs: "ca ts"
"ki tt en s_" (_ represents a space)
2. into ints: 25441 29811
27497 29812 25966 29472
3. XOR with 31337: 6408 3610
4352 3613 7943 2377
Decryption is performed with the same steps, but in reverse order.
• The Ferocious Kittens have intercepted two secret messages from Dougie Dog:
15643 6913 6916 23040 2377 6985 6408 3657 5638 3084 2119
15910 23079 13629 23101 10300 10557 23073 13092 23369
• Write a program that decrypts them.
(hint: this will be a lot easier if you begin by writing a program to encrypt values -
- you can check each step with "cats" and "kittens" to make sure you understand
the process!)
• You must use a function to split a large integer into two separate letters. This
function may not print anything to the screen.
(hint: how can a function return two values?)
Note: Show your work to a demonstrator/GTA.