Exam Frequency Analysis
Past paper frequency (2018 to 2024)
This topic accounts for approximately 6% of your exam marks.
stable
Low
Stable6%
Writing Boolean expressions from logic diagrams and simplifying using laws appear regularly.
De Morgan's Laws describe what happens when a NOT is applied to a whole bracket. They are the most important pair of laws for IGCSE simplification questions.
De Morgan #1:
¬(A · B) = ¬A + ¬BDe Morgan #2:
¬(A + B) = ¬A · ¬B
In words: distribute the NOT onto every variable in the bracket, then flip the connective (· becomes +, and + becomes ·).
A two-step recipe that always works:
- Put a
¬on every variable inside the bracket. - Flip the connective: AND becomes OR, or OR becomes AND.
Example — simplify ¬(A · B) using De Morgan's.
Step 1: negate each variable → ¬A and ¬B.
Step 2: flip the connective from · to + → ¬A + ¬B.
So ¬(A · B) = ¬A + ¬B. That is exactly the definition of a NAND gate.
Example — simplify ¬(A + B).
Step 1: negate each variable → ¬A and ¬B. Step 2: flip + to · → ¬A · ¬B. That is exactly the definition of a NOR gate.
De Morgan's laws extend to more than two variables:
¬(A · B · C) = ¬A + ¬B + ¬C¬(A + B + C) = ¬A · ¬B · ¬C
Example — a longer rearrangement: rewrite ¬(¬A · B) so the only NOTs are on individual variables.
Apply De Morgan: ¬(¬A · B) = ¬(¬A) + ¬B.
Now use double negation: ¬(¬A) = A. So the answer is A + ¬B.