Digital Electronics Unit 2 Notes | Minimization Techniques & Logic Gates | RTU B.Tech 3rd Semester
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In this post, you will get complete, exam-oriented and easy-to-understand notes for
Digital Electronics – Unit 2 as per the
Rajasthan Technical University (RTU), Kota syllabus.
These notes are prepared for 10–15 mark questions with step-by-step explanations, definitions, and methods.
📜 RTU Official Syllabus – Unit 2
Course Code: 3CS3-04 – Digital Electronics
Semester: III (B.Tech CSE)
Credits: 3 | Max Marks: 100
End Term Exam: 3 Hours
Unit-2: Minimization Techniques and Logic Gates
• Principle of Duality
• Boolean Expressions
• Minimization of Boolean Expressions
• Minterm and Maxterm
• SOP and POS forms
• Karnaugh Map (K-Map) Minimization
• Don’t Care Conditions
• Quine-McCluskey Method
🎥 Digital Electronics Unit 2 – Complete Video Lecture
👉 Watch this lecture for K-Map solving, SOP/POS concepts, and exam tricks.
📘 Unit 2: Minimization Techniques & Logic Gates (Easy Notes)
1️⃣ Principle of Duality
The Principle of Duality states that every Boolean expression remains valid if we interchange:
- AND (·) ↔ OR (+)
- 0 ↔ 1
Example:
Original: A + 0 = A
Dual: A · 1 = A
Exam Use: Asked directly for 5 marks.
2️⃣ Boolean Expression
A Boolean Expression is an algebraic expression formed using:
- Binary variables (0 or 1)
- Logic operators: AND, OR, NOT
Example:
F = A·B + C'
3️⃣ Minimization of Boolean Expressions
Minimization means reducing a Boolean expression to its simplest form to use fewer logic gates.
Advantages:
- Less hardware cost
- Reduced power consumption
- Faster operation
4️⃣ Minterm and Maxterm
🔹 Minterm
A minterm is a product (AND) of all variables in true or complemented form that gives output 1.
Example: A·B·C'
🔹 Maxterm
A maxterm is a sum (OR) of all variables that gives output 0.
Example: (A + B' + C)
5️⃣ SOP and POS Forms
🔹 Sum of Products (SOP)
OR operation of multiple minterms.
Example: F = A·B + B·C
🔹 Product of Sums (POS)
AND operation of multiple maxterms.
Example: F = (A + B)(B + C)
Exam Tip: SOP is more commonly used.
6️⃣ Karnaugh Map (K-Map) Minimization
A Karnaugh Map is a graphical method to simplify Boolean expressions.
- 2-variable K-Map → 4 cells
- 3-variable K-Map → 8 cells
- 4-variable K-Map → 16 cells
Rules:
- Group 1, 2, 4, 8 cells
- Groups must be rectangular
- Larger groups give simpler expressions
7️⃣ Don’t Care Conditions
Don’t care conditions are input combinations that never occur or are irrelevant.
They are marked as X in K-Maps and help in better minimization.
8️⃣ Quine-McCluskey Method
The Quine-McCluskey Method is a tabular method used for large number of variables.
Steps:
- List minterms in binary form
- Group by number of 1s
- Combine terms
- Find prime implicants
Exam Use: Theory question (no numericals usually).
📕 Download Digital Electronics Unit 2 Notes (PDF)
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