Boolean Logic Class 11 CBSE Computer Science: NOT, AND, OR, NAND, NOR, XOR, Truth Tables, De Morgan's Laws and Logic Circuits
Class 11 · Computer Science
Boolean Logic (CBSE Class 11 Computer Science)
Computers make decisions based on logical conditions. These conditions have only two possible values: True or False. Boolean Logic provides the mathematical foundation for decision-making in computers and digital electronics. It is widely used in programming, logic circuits, and computer architecture.
Learning Objectives
- Understand Boolean Logic.
- Learn Boolean values.
- Study NOT, AND, OR, NAND, NOR and XOR operators.
- Understand truth tables.
- Learn De Morgan's Laws.
- Understand logic circuits.
What is Boolean Logic?
Boolean Logic is a branch of mathematics developed by George Boole. It deals with logical values that have only two possible states: True (1) and False (0).
Boolean Values
| Value | Meaning |
|---|---|
| 1 | True / ON / High |
| 0 | False / OFF / Low |
Boolean Operators
The most commonly used Boolean operators are:
- NOT
- AND
- OR
- NAND
- NOR
- XOR
NOT Gate
The NOT gate is a unary operator. It reverses the input value.
Logic Symbol
A ───▷o── Y
Boolean Expression
Y = NOT A
or
Y = A'
Truth Table
| A | Y |
|---|---|
| 0 | 1 |
| 1 | 0 |
AND Gate
The AND gate produces True only when both inputs are True.
::contentReference[oaicite:0]{index=0}Boolean Expression
Y = A AND B
or
Y = A · B
Truth Table
::contentReference[oaicite:1]{index=1}| A | B | Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
OR Gate
The OR gate produces True if at least one input is True.
Boolean Expression
Y = A OR B
or
Y = A + B
Truth Table
| A | B | Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
NAND Gate
The NAND gate is the complement of the AND gate. It produces False only when both inputs are True.
Boolean Expression
Y = (A · B)'
Truth Table
| A | B | Y |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
NOR Gate
The NOR gate is the complement of the OR gate. It produces True only when both inputs are False.
Boolean Expression
Y = (A + B)'
Truth Table
| A | B | Y |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
XOR (Exclusive OR) Gate
The XOR gate produces True only when the two inputs are different.
Boolean Expression
Y = A ⊕ B
Truth Table
| A | B | Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Comparison of Logic Gates
| Gate | Condition for Output = 1 |
|---|---|
| NOT | Input is 0 |
| AND | Both inputs are 1 |
| OR | At least one input is 1 |
| NAND | Both inputs are not 1 |
| NOR | Both inputs are 0 |
| XOR | Inputs are different |
De Morgan's Laws
De Morgan's Laws simplify Boolean expressions and are widely used in logic circuit design.
(A · B)' = A' + B'
(A + B)' = A' · B'
Verification of First De Morgan's Law
| A | B | (A·B)' | A'+B' |
|---|---|---|---|
| 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
Verification of Second De Morgan's Law
| A | B | (A+B)' | A'·B' |
|---|---|---|---|
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 |
Logic Circuits
A Logic Circuit is an electronic circuit made using one or more logic gates to perform logical operations on binary inputs.
Example 1: AND Circuit
A ─────┐
│AND──► Output
B ─────┘
Example 2: OR Circuit
A ─────┐
│OR──► Output
B ─────┘
Example 3: NOT Circuit
A ──NOT──► Output
Real-Life Examples
- AND Gate: A locker opens only when both passwords are correct.
- OR Gate: A room light can be switched ON using either of two switches.
- NOT Gate: An automatic street light turns ON when there is no sunlight.
- XOR Gate: A staircase light changes its state when either switch is pressed.
Common Errors
- Confusing OR with XOR.
- Writing incorrect truth tables.
- Interchanging NAND and NOR gates.
- Applying De Morgan's Laws incorrectly.
- Forgetting that NOT is a unary operator.
Exam Tips
- Memorize all six truth tables.
- Practice De Morgan's Laws regularly.
- Remember that NAND and NOR are universal gates.
- Understand the difference between OR and XOR.
- Learn Boolean expressions for each gate.
Frequently Asked Questions (FAQs)
1. What is Boolean Logic?
Boolean Logic is a system of logic that uses only two values: True (1) and False (0).
2. Who developed Boolean Logic?
George Boole developed Boolean Logic.
3. Which gate is called a universal gate?
Both NAND and NOR are called universal gates because any logic circuit can be constructed using only NAND gates or only NOR gates.
4. What is the difference between OR and XOR gates?
OR gives an output of 1 if at least one input is 1, whereas XOR gives an output of 1 only when the two inputs are different.
5. Why are De Morgan's Laws important?
They simplify Boolean expressions and help in designing efficient logic circuits.
Summary
- Boolean Logic is based on two values: 0 (False) and 1 (True).
- The six important logic gates are NOT, AND, OR, NAND, NOR, and XOR.
- Truth tables describe the output for every possible input combination.
- De Morgan's Laws are used to simplify Boolean expressions.
- Logic circuits use logic gates to perform decision-making operations in digital systems.
- Boolean Logic forms the foundation of modern computers and digital electronics.