⚡ Test 3 – Boolean Algebra

📅 Test Details

📚 Topics Covered

• Boolean functions and truth tables
• Normal forms (DNF, CNF)
• Logic gates and circuits
• Karnaugh maps for minimization
• Boolean simplification using laws
• Functional completeness

🎯 Sample Problem Types

• Truth Tables: Construct truth table for given Boolean expression
• Normal Forms: Convert given function to DNF and CNF
• Simplification: Simplify Boolean expressions using laws
• Circuits: Design circuit for majority function
• K-Maps: Use K-map to minimize given function
• Completeness: Prove {NAND} is functionally complete

📖 Preparation Guide

Review Materials

1. Lecture Notes: Module 3 (Boolean Algebra)
2. Homework: HW 3
3. Textbook: Kenneth Rosen

Practice Problems

• Truth Tables: Build tables for 5–10 complex expressions
• DNF/CNF: Convert between forms for various functions
• Boolean Laws: Simplify 10+ expressions step-by-step
• Circuits: Draw circuits for common functions (adders, multiplexers)
• K-Maps: Minimize 20+ random functions (including don’t cares)
• Completeness: Practice expressing AND, OR, NOT with NAND

Common Pitfalls

⚠️ Watch Out!

• De Morgan’s Laws: \( \overline{x \vee y} = \overline{x} \wedge \overline{y} \), and \( \overline{x \wedge y} = \overline{x} \vee \overline{y} \)
• K-map groupings: must be rectangles with power-of-2 sizes (1, 2, 4, 8…)
• Circuit notation: distinguish AND from OR gate symbols
• DNF vs CNF: DNF is OR of ANDs; CNF is AND of ORs
• Don’t forget: NOT gate inverts (circles on circuit diagrams)

💡 Pro Tips

• Truth tables first – when stuck, build truth table
• K-maps are visual – look for largest groupings first
• Simplify before circuits – smaller expressions = fewer gates
• Test with cases – verify circuit with sample inputs
• Know your laws – memorize De Morgan’s, distributive, absorption
• Draw clearly – messy circuits lead to errors