Complete Boolean Logic Study Guide
1. What is Boolean Logic?
Boolean logic is the foundation of digital electronics. It uses only two values: 1 (ON / TRUE) and 0
(OFF / FALSE). Computers and digital circuits make decisions using Boolean logic.
2. Logic Gates
AND Gate: Output is 1 only if ALL inputs are 1.
OR Gate: Output is 1 if at least one input is 1.
NOT Gate: Output is the opposite of the input.
NAND Gate: NOT of AND.
NOR Gate: NOT of OR.
XOR Gate: Output is 1 if inputs are different.
3. Truth Tables
Truth tables list all possible input combinations and their outputs.
2 inputs → 4 rows
3 inputs → 8 rows
Each row represents a condition of the circuit.
4. Boolean Expressions (Logic Expressions)
Boolean expressions describe logic behavior using AND, OR, and NOT.
Example:
NOT A AND B OR C
5. Converting Truth Tables to Logic Expressions
Step 1: Identify rows where output = 1.
Step 2: For each row: - Input = 0 → NOT - Input = 1 → normal - Combine inputs with AND.
Step 3: Combine all rows using OR.
6. Example (3 Inputs)
Row: A=0, B=1, C=0 → Output=1
Logic expression:
NOT A AND B AND NOT C
7. Boolean Simplification (Basic Rules)
A AND 1 = A
A OR 0 = A
A AND NOT A = 0
A OR NOT A = 1
Simplifying reduces the number of gates.
8. Logic Circuits
Logic circuits are built using gates.
Steps to draw a circuit: 1. Draw NOT gates first. 2. Draw AND gates for conditions. 3. Combine
using OR gates. 4. Label all inputs and outputs clearly.
9. Exam Tips
- Every output=1 row becomes one AND condition.
- Use NOT only when input is 0.
- Simplify expressions when possible.
- Practice drawing neat logic diagrams.