Lab 2 – Active Logic & Formula Programs

PSUC Lab 2 — Formula & Arithmetic Expressions

Active Logic & Mathematical C Programming

In Lab 2, we bridge real-world math formulas into C code expressions. Master integer division truncation, modulus remainder operator, floating point division, and <math.h> functions!

Essential C Formula Rules

Operator / Function	C Syntax	Key Rule & Trap
Integer Division	`a / b`	Truncates decimal! `7 / 2 = 3` (Not 3.5)
Modulus (Remainder)	`a % b`	Only works on integers! `7 % 2 = 1`
Float Division	`5.0 / 9.0`	Writing `5 / 9` in C yields `0`! Use floats.
Square Root	`sqrt(x)`	Header: `#include <math.h>`
Power Function	`pow(base, exp)`	Header: `#include <math.h>`

🎯 Learning Philosophy: Active Logic Building

Instead of copy-pasting code, each experiment in Lab 2 features 3 Interactive Learning Modes:

🧠 Tab 1 (Logic & Hints): Understand the math formula & step-by-step pseudo-code.
🧩 Tab 2 (Logic Puzzle): Fill in missing operators/variables & run live simulations.
💻 Tab 3 (C Solution): Verify your answer against verified C source code.

Use the mode tabs on each slide to test your logic before looking at full code!

Program 1 of 6

To Convert Seconds into Hours, Minutes & Seconds

Given total seconds S, extract whole hours using S / 3600, remaining minutes using (S % 3600) / 60, and leftover seconds using S % 60.

Mathematical Formula Breakdown

1 Hour = 3600 seconds
1 Minute = 60 seconds
Hours: H = total_sec / 3600 (Integer division truncates decimal)
Remaining Sec after Hours: rem = total_sec % 3600
Minutes: M = rem / 60
Leftover Seconds: S = rem % 60

Interactive Logic Hints

💡 Hint 1: Why do we use integer division / for Hours? ▼

In C, 3665 / 3600 gives 1 (whole hour). It automatically drops the .018 decimal part!

💡 Hint 2: How does % (modulus) help pass remaining time? ▼

3665 % 3600 gives 65 (the seconds left over after removing 1 full hour). Then 65 / 60 = 1 min and 65 % 60 = 5 sec.

🧩 Complete the Missing Formula Logic

Fill in the missing C operators/constants below and test your logic:

h = total_sec 3600;
rem = total_sec 3600;
m = rem / ;
s = rem 60;

Select operators above and click Check!

⏱️ Live Time Converter Simulator

Total Seconds Input:

Result will appear here...

seconds_converter.cReference C Code

#include <stdio.h>

int main() {
    int total_sec, hours, minutes, seconds, rem;
    
    printf("Enter total seconds: ");
    scanf("%d", &total_sec);
    
    hours   = total_sec / 3600;     // 1 hour = 3600 seconds
    rem     = total_sec % 3600;     // Remaining seconds
    minutes = rem / 60;             // 1 minute = 60 seconds
    seconds = rem % 60;             // Leftover seconds
    
    printf("%d sec = %d Hours, %d Mins, %d Secs\n", total_sec, hours, minutes, seconds);
    return 0;
}

Program 2 of 6

To Find the Sum of Digits of a Number

Extract digits from right to left: digit = n % 10 isolates the last digit, and n = n / 10 drops it.

Digit Peel Algorithm (Base 10)

Extract Last Digit: 1234 % 10 = 4
Accumulate: sum = sum + digit (0 + 4 = 4)
Remove Last Digit: 1234 / 10 = 123 (Integer truncation drops .4)
Repeat loop until n == 0!

Interactive Logic Hints

💡 Hint 1: Why does % 10 always give the last digit? ▼

In base 10 decimal system, remainder after dividing by 10 is always the ones-place digit (e.g. 589 % 10 = 9).

💡 Hint 2: What happens when n becomes single digit (e.g. 5)? ▼

5 % 10 = 5 (extracts 5), then 5 / 10 = 0. Loop condition n > 0 becomes false and loop stops cleanly!

🧩 Complete the Digit Extraction Code

while (temp > 0) {
  digit = temp ;
  sum = sum digit;
  temp = temp 10;
}

Select operators above and click Check!

🔢 Visual Step-by-Step Digit Trace

Enter integer n:

Trace will show here...

digit_sum.cReference C Code

#include <stdio.h>

int main() {
    int num, temp, sum = 0, digit;
    
    printf("Enter a number: ");
    scanf("%d", &num);
    
    temp = num;
    while (temp > 0) {
        digit = temp % 10;    // Extract last digit
        sum  += digit;         // Add to running sum
        temp  = temp / 10;    // Drop last digit
    }
    
    printf("Sum of digits of %d = %d\n", num, sum);
    return 0;
}

Program 3 of 6

Temperature Converter (°F ↔ °C)

Beware of integer division trap! Writing 5 / 9 in C evaluates to 0. You must use floating-point literal 5.0 / 9.0.

Conversion Formulas

Fahrenheit to Celsius: C = (F - 32) * 5.0 / 9.0
Celsius to Fahrenheit: F = (C * 9.0 / 5.0) + 32
Format Specifier for 2 decimals: %.2f

Interactive Logic Hints

💡 Hint 1: What is the classic C integer division trap here? ▼

If you write (F - 32) * (5 / 9), C evaluates integer division 5 / 9 = 0, making Celsius result ALWAYS 0.00!

💡 Hint 2: How to fix integer division? ▼

Write 5.0 / 9.0 (with decimal point). This forces C to perform floating-point division (0.5556).

🧩 Complete the Temperature Calculation

float F = 98.6, C;
// Choose correct float constants:
C = (F - 32.0) * ;

Select formula above and click Check!

🌡️ Dual Temp Simulator

Fahrenheit (°F):

Celsius (°C):

Result live update...

temp_convert.cReference C Code

#include <stdio.h>

int main() {
    float fahrenheit, celsius;
    
    printf("Enter temp in Fahrenheit: ");
    scanf("%f", &fahrenheit);
    
    // Note: Use 5.0 / 9.0 for float division
    celsius = (fahrenheit - 32.0) * 5.0 / 9.0;
    
    printf("%.2f°F = %.2f°C\n", fahrenheit, celsius);
    return 0;
}

Program 4 of 6

Distance Between Two Points (x1, y1) & (x2, y2)

Uses Euclidean distance formula d = √((x₂ - x₁)² + (y₂ - y₁)²) with <math.h> functions sqrt() and pow().

Euclidean Distance Formula

Header required: #include <math.h>
Square Root: sqrt(x)
Power: pow(x, 2) computes x²
Expression: dist = sqrt(pow(x2 - x1, 2) + pow(y2 - y1, 2))

Interactive Logic Hints

💡 Hint 1: Can we write (x2 - x1)*(x2 - x1) instead of pow()? ▼

Yes! (x2 - x1) * (x2 - x1) is faster than pow() because it avoids library function call overhead.

💡 Hint 2: What data type should distance be? ▼

Use double (with %lf in scanf) for highest precision when calculating square roots!

🧩 Complete Distance Calculation Code

#include <stdio.h>
#include <>

dist = ((x2 - x1, 2) + pow(y2 - y1, 2));

Fill in functions above and click Check!

📍 Coordinate Distance Calculator

x1:

y1:

x2:

y2:

Distance = 5.0000

point_distance.cReference C Code

#include <stdio.h>
#include <math.h>   // Required for sqrt() & pow()

int main() {
    double x1, y1, x2, y2, distance;
    
    printf("Enter x1 y1: ");
    scanf("%lf %lf", &x1, &y1);
    printf("Enter x2 y2: ");
    scanf("%lf %lf", &x2, &y2);
    
    distance = sqrt(pow(x2 - x1, 2) + pow(y2 - y1, 2));
    
    printf("Distance = %.4lf\n", distance);
    return 0;
}

Program 5 of 6

Area & Circumference of a Circle

Compute Area = πr² and Circumference = 2πr using constant macro #define PI 3.14159.

Circle Formulas

Macro Constant: #define PI 3.14159265
Area: area = PI * r * r
Circumference: circumference = 2 * PI * r

Interactive Logic Hints

💡 Hint 1: What does #define macro do? ▼

Preprocessor replaces every occurrence of PI in your code with 3.14159265 before compilation!

🧩 Complete the Circle Geometry Equations

#define PI 3.14159
float r = 7.0, area, circum;
area = PI * ;
circum = * PI * r;

Select formulas above and click Check!

⭕ Circle Geometry Calculator

Radius (r):

Result live update...

circle_calc.cReference C Code

#include <stdio.h>
#define PI 3.14159265359

int main() {
    float radius, area, circumference;
    
    printf("Enter radius of circle: ");
    scanf("%f", &radius);
    
    area          = PI * radius * radius;
    circumference = 2 * PI * radius;
    
    printf("Area          = %.2f sq. units\n", area);
    printf("Circumference = %.2f units\n", circumference);
    return 0;
}

Program 6 of 6

Swap Two Variables (With & Without 3rd Variable)

Compare standard variable swap using temp vs arithmetic swap without third variable.

Swapping Methods

Method 1 (Temp Var): temp = a; a = b; b = temp;
Method 2 (Arithmetic): a = a + b; b = a - b; a = a - b;

Interactive Logic Hints

💡 Hint 1: How does arithmetic swapping work? ▼

If a=10, b=20: a = 30. Then b = 30 - 20 = 10. Then a = 30 - 10 = 20. Result: swapped!

🧩 Complete Arithmetic Swap Equations

int a = 10, b = 20;
a = a b; // a becomes 30
b = a b; // b becomes original a (10)
a = a b; // a becomes original b (20)

Select operators above and click Check!

🔄 Memory Swap Simulator

a =

b =

Trace will show here...

swap_methods.cReference C Code

#include <stdio.h>

int main() {
    int a = 10, b = 20, temp;
    
    // Method 1: Using 3rd variable
    temp = a;
    a    = b;
    b    = temp;
    printf("Method 1 Swap: a=%d, b=%d\n", a, b);
    
    // Method 2: Without 3rd variable (Arithmetic)
    a = a + b;
    b = a - b;
    a = a - b;
    printf("Method 2 Swap: a=%d, b=%d\n", a, b);
    
    return 0;
}

Knowledge Check

Test Your Formula & Operator Mastery

Question 1 of 5

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