Last Updated: 28/07/2021

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Lesson 8 - Mathematics

Lessons >> Basics >> Lesson 8 - Mathematics

Lesson Contents

Basic mathematics
Addition
Subtraction
Multiplication
Division
Learning how mathematics can lead to overflows in a numeric variable
The use of a 'long'
How to get a 'long' answer from 'int' variables
Basic errors in changing an 'int' to a 'long'
How to run something once in the main loop using an 'if' statement
Dealing with values after the decimal point
Using a 'float' data type
How to get a 'float' for an 'int'
Common problems in getting a 'float' for an 'int'

Example 1: mathematics1.ino

Click to Download code:mathematics1.ino

Addition)
Data overuns
Creating a 'long' from the addition of int's
Common errors when creating a long from int.
Getting code to run once in the main loop using an 'if' statement

 
/* 24/07/2021
   mathematicsv1

   Addition,
   how to make something run once in the main loop.
   importance of commenting code
   How integers can over run with addition

*/

int q;
int w;
int myAnswer;
long myLongAnswer;

void setup() {
  // Serial.begin(9600) starts serial communication. 9600bps bits per second = 1200 characters per second
  Serial.begin(9600);
  //Send script name
  Serial.println("mathematicsv1...");
  //this will print a blank line
  Serial.println(" ");

}

void loop() {
  if (q < 1) {
    //Example 1
    //add 1 to the value of q so the if statement will fail next time round
    q++;
    Serial.print("q = ");
    Serial.println(q);
    //Simple addition
    Serial.println("Simple addition");
    for (w = 0; w < 10; w++) {
      myAnswer =  w + q;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myAnswer =");
      Serial.println(myAnswer);
    }
    
    //Example 2
    //change the value of q to 32760
    q = 32760;
    Serial.println("Simple addition...The problem of overflowing the variable type");
    Serial.print("q = ");
    Serial.print(q);
    for (w = 0; w < 10; w++) {
      myAnswer =  w + q;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myAnswer =");
      Serial.println(myAnswer);
    }
    //Example 3
    q = 32760;
    Serial.println("Simple addition... 2 integers don't make a long");
    Serial.print("q = ");
    Serial.print(q);
    for (w = 0; w < 10; w++) {
      myLongAnswer =  w + q;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myLongAnswer =");
      Serial.println(myLongAnswer);
    }
    
    //Example 4
    q = 32760;
    Serial.println("Simple addition... 2 integers converted to a long");
    Serial.print("q = ");
    Serial.print(q);
    for (w = 0; w < 10; w++) {
      myLongAnswer =  long(w) + long(q);
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myLongAnswer =");
      Serial.println(myLongAnswer);
    }

  }

}

Example 2: mathematicsv2.ino

Click to Download code:mathematicsv2.ino

Subtraction.
Issues with subtracting a negative number
Negative data overruns .

 
/* 24/07/2021
   mathematicsv2

   Subtraction 
    How integers can over run with subtraction

*/

int q;
int w;
int myAnswer;


void setup() {
  // Serial.begin(9600) starts serial communication. 9600bps bits per second = 1200 characters per second
  Serial.begin(9600);
  //Send script name
  Serial.println("mathematicsv2...");
  //this will print a blank line
  Serial.println(" ");

}

void loop() {
  if (q < 1) {
    //Example 1
    //make q = 1 so the if statement will fail next time round
    q = 1;
    Serial.print("q = ");
    Serial.println(q);
    //Simple addition
    Serial.println("Simple subtraction");
    for (w = 0; w < 10; w++) {
      myAnswer =  w - q;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myAnswer =");
      Serial.println(myAnswer);
    }
    //Example 2
    q = -10;
    Serial.println("Simple subtraction... - negative number double negative = positive");
    Serial.print("q = ");
    Serial.println(q);
    for (w = 0; w < 10; w++) {
      myAnswer =  w - q;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myAnswer =");
      Serial.println(myAnswer);
    }
    //Example 3
    q = -10;
    Serial.println("Simple subtraction...negative numbers");
    Serial.print("q = ");
    Serial.println(q);
    for (w = 0; w < 10; w++) {
      myAnswer =  q - w;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myAnswer =");
      Serial.println(myAnswer);
    }
    //example 4
    //change the value of q to 32760
    q = -32760;
    Serial.println("Simple subtraction...The problem of overflowing the variable type");
    Serial.print("q = ");
    Serial.println(q);
    for (w = 0; w < 10; w++) {
      myAnswer =  q - w;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myAnswer =");
      Serial.println(myAnswer);
    }
    
    //make q equal to 1 to make sure the if loop does not run again
    q = 1;
  }

}

Example 3: mathematicsv3.ino

Click to Download code:mathematicsv3.ino

Multiplication.
Strange values from data over runs
Getting a 'long' answer from multiplication of 'int's'

 
/* 24/07/2021
   mathematicsv3

   Multiplication
   How integers can over run with multiplication and give very unexpected results

*/

int q;
int w;
int myAnswer;
long myLongAnswer;

void setup() {
  // Serial.begin(9600) starts serial communication. 9600bps bits per second = 1200 characters per second
  Serial.begin(9600);
  //Send script name
  Serial.println("mathematicsv3...");
  //this will print a blank line
  Serial.println(" ");

}

void loop() {
  if (q < 1) {
    //Example 1
    //make q = 1 so the if statement will fail next time round
    q = 1;
    Serial.print("q = ");
    Serial.print(q);
    //Simple multiplication
    Serial.println("Simple multiplication");
    for (w = 0; w < 10; w++) {
      // the symbol for multiplication is *
      myAnswer =  w * q;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myAnswer =");
      Serial.println(myAnswer);
    }

    //change the value of q to 32760
    q = 32760;
    //the answer can be positive or negative depending on the amount of over run.
    Serial.println("Simple multiplication...The problem of overflowing the variable type");
    Serial.print("q = ");
    Serial.print(q);
    for (w = 0; w < 10; w++) {
      myAnswer =  w * q;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myAnswer =");
      Serial.println(myAnswer);
    }
    //Example 3
    //change the value of q to 32760
    q = 32760;
    Serial.println("Simple multiplication... 2 integers converted to a long");
    Serial.print("q = ");
    Serial.print(q);
    for (w = 0; w < 10; w++) {
      myLongAnswer =  long(w) * long(q);
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myLongAnswer =");
      Serial.println(myLongAnswer);
    }



  }

}

Example 4: mathematicsv4.ino

Click to Download code:mathematicsv4.ino

Division
Problems with results being rounded down
Using the 'float' variable type
Converting divided int's into a float
Common problems when converting numbers to a float.
Increasing the number of values beyind the decimal point when printing to the Serial monitor.
Remember Arduinos don't like numbers with decimal points.
Alternates to using a float by multiplying values by 100 or 1000.

 
/* 24/07/2021
   mathmaticsv4

   Division
   Understand the issues with division of integers.
   learn how to use a float.
   Arduinos do NOT like floats, they use a lot of processor time compared to whole numbers.

*/

int q;
int w;
int myAnswer;
float myFloat;

void setup() {
  // Serial.begin(9600) starts serial communication. 9600bps bits per second = 1200 characters per second
  Serial.begin(9600);
  //Send script name
  Serial.println("mathematicsv4...");
  //this will print a blank line
  Serial.println(" ");

}

void loop() {
  if (q < 1) {
    //Example 1
    //add 1 to the value of q so the if statement will fail next time round
    q++;
    Serial.print("q = ");
    Serial.println(q);
    //Simple addition
    Serial.println("Simple division");
    for (w = 0; w < 10; w++) {
      // the symbol for division is /
      myAnswer =  w / q;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myAnswer =");
      Serial.println(myAnswer);
    }
    //Example 2
    //change the value of q to 10
    q = 10;
    //Notice that an integer cannot have a decimal point
    Serial.println("Simple division...all the results are rounded down.");
    Serial.print("q = ");
    Serial.println(q);
    for (w = 0; w < 31; w++) {
      myAnswer =  w / q;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myAnswer =");
      Serial.println(myAnswer);
    }
    //Example 3
    //change the value of q to 10
    q = 10;
    //Notice that an integer cannot have a decimal point

    //helps with the issue of dividing and then multiplying
    Serial.println("Simple division...multiplying by 100 to use a whole number.");
    Serial.print("q = ");
    Serial.println(q);
    for (w = 0; w < 31; w++) {
      myAnswer =  w * 100 / q;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myAnswer =");
      Serial.println(myAnswer);
    }
    //Example 4
    //change the value of q to 10
    q = 10;
    //Using a float to get a decimal point
    Serial.println("Simple division...Using a float");
    Serial.print("q = ");
    Serial.println(q);
    for (w = 0; w < 31; w++) {
      //because the division is between two integers there is no decimal value even when we save the result as a float.
      myFloat =  w / q;
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myFloat =");
      Serial.println(myFloat);
    }
    //Example 4
    q = 10;
    //Using a flat to get a decimal point
    Serial.println("Simple division...Using a float");
    Serial.print("q = ");
    Serial.println(q);
    for (w = 0; w < 31; w++) {
      myFloat =  float(w) / float(q);
      Serial.print(" w =");
      Serial.print(w);
      Serial.print(" myFloat =");
      //Only prints to 2 decimal places by default
      Serial.print(myFloat);
      Serial.print(" myFloat to 4 decimal points =" );
      Serial.println(myFloat,4);
    }

  }

}

Additional Resource Links

Don't forget to use the Reference in you Arduino IDE and look at Arithmetic for more help on this lesson.

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