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Ahmed Rakan
Ahmed Rakan

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Simplifying If Statements with Binary Algebra

#programming #dsa

If statements are one of the most common constructs in programming — but they can get messy fast. Nested ifs, long logical chains, and hard-to-read conditions make code brittle and harder to maintain. Luckily, binary algebra (Boolean algebra) provides a powerful set of tools to simplify these conditions.

Let’s break this down in a beginner-friendly way.

What is Binary Algebra?

Binary (or Boolean) algebra deals with values that can be either true or false. The three basic operations are:

  • AND ( ∧ ) – true only if both sides are true.
  • OR ( ∨ ) – true if at least one side is true.
  • NOT ( ¬ ) – inverts the value (true becomes false, false becomes true).

In most programming languages, these are written as:

  • && for AND
  • || for OR
  • ! for NOT

Binary/Boolean Algebra have set of rules to implement :

Boolean Algebra rules

The Problem: Complex If Statements

Consider this code:

if ((isAdmin && !isBanned) || (isModerator && !isBanned)) {
  grantAccess();
}
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At first glance, this looks fine — but there’s repetition here. The !isBanned check is repeated twice.

As well we can boost performance by implementing short circuit pattern.

We can say whenever the user is indeed banned there is no point of evaluating the other part.

And that's both makes our program clearer and faster to execute.

Step 1: Factor Out Common Conditions

Using Boolean algebra, we can factor like we do in math:

(A && C) || (B && C)  ⟶  (A || B) && C
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Applying this:

if ((isAdmin || isModerator) && !isBanned) {
  grantAccess();
}
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Now the condition is shorter, clearer, and easier to maintain.

Step 2: Apply De Morgan’s Laws

Sometimes we have a negation on a group:

if (!(isWeekend || isHoliday)) {
  work();
}
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De Morgan’s Law lets us distribute the NOT:

¬(A ∨ B) = ¬A ∧ ¬B
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Which becomes:

if (!isWeekend && !isHoliday) {
  work();
}
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This is easier to read because each part is now explicitly checked.

Key Takeaways

  • Factor common logic to avoid repetition.
  • Use De Morgan’s laws to make negated conditions explicit.
  • Eliminate redundant checks for clarity and efficiency.
  • Use truth tables when in doubt to verify your logic.

Simplifying if statements makes your code cleaner, easier to read, and less prone to bugs. The next time you see a messy if, try applying these rules — your future self (and your teammates) will thank you!

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