Boolean Algebra and Binary Arithmetic

📑 Navigation

1. Key Takeaways
2. George Boole and Historical Context
3. Algebra as a System
4. Operator Overloading
5. Decimal Addition Review
6. Binary Addition
7. Half Adder Circuit
8. Full Adder Circuit
9. Ripple Carry Adder
10. XOR Connection to Addition
11. Circuit Design Trade-offs
12. Number Representation Limits
13. Overflow and Underflow

Key Takeaways

🎯 Main Takeaway #1: Boolean algebra is NOT the same as binary arithmetic. The same symbols (+ and ·) mean different things in different contexts.

🎯 Main Takeaway #2: N-bit representation can store values from 0 to 2^N - 1. Limited representation space causes overflow and underflow problems.

✅ Boolean algebra ≠ binary arithmetic - different systems with different rules