Logic gates are the building blocks of digital circuits. Learn types, symbols, Boolean expressions, truth tables, universal gates, key laws, and uses.
What Are Logic Gates?
Logic gates are the fundamental building blocks of digital electronics. They take one or more binary inputs (0 or 1) and produce a single binary output according to a logical rule. You will find them everywhere: calculators, microprocessors, ALUs, memory, control systems, and embedded devices. In binary logic, 1 represents True/High/ON and 0 represents False/Low/OFF.
Binary Logic Refresher
- 1 (True, High, ON)
- 0 (False, Low, OFF)
Digital circuits interpret and combine these values using gate rules to form complex systems (adders, multiplexers, CPUs).
Core Types of Logic Gates (Symbols, Expressions, Truth Tables)
Below are the seven standard gates with concise definitions, Boolean expressions, and truth tables you can use directly in class or labs.
AND Gate (⋅)
- Boolean Expression: Y=A⋅BY = A \cdot BY=A⋅B
- Meaning: Output is 1 only if both inputs are 1.
| A | B | Y = A⋅B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
OR Gate (+)
- Boolean Expression: Y=A+BY = A + BY=A+B
- Meaning: Output is 1 if any input is 1.
| A | B | Y = A+B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
NOT Gate (¬ or A’)
- Boolean Expression: Y=A’
- Meaning: Inverts the input.
| A | Y = A’ |
|---|---|
| 0 | 1 |
| 1 | 0 |
NAND Gate (AND + NOT)
- Boolean Expression: Y=(A⋅B)’
- Meaning: Opposite of AND.
| A | B | Y = (A⋅B)’ |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
NOR Gate (OR + NOT)
- Boolean Expression: Y=(A+B)’
- Meaning: Opposite of OR.
| A | B | Y = (A+B)’ |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
XOR Gate (⊕)
- Boolean Expression: Y=A⊕B=A’B+AB’
- Meaning: Output is 1 only when inputs differ.
| A | B | Y = A⊕B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
XNOR Gate (⊙)
- Boolean Expression: Y=A⊙B=AB+A’B’
- Meaning: Output is 1 only when inputs are the same.
| A | B | Y = A⊙B |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Universal Gates: NAND and NOR
NAND and NOR are called universal gates because any Boolean function (and therefore any circuit) can be implemented using only NAND or only NOR gates. This is crucial in IC design and optimization because a single gate type can reduce manufacturing complexity and cost.
Quick Review of Boolean Algebra Laws
- Identity: A+0=A , A⋅1=A
- Null (Dominance): A+1=1 , A⋅0=0
- Idempotent: A+A=A , A⋅A=A
- Inverse: A+A’=1 , A⋅A’=0
- Commutative: A+B=B+A , A⋅B=B⋅A
- Distributive: A⋅(B+C)=AB+AC
You will repeatedly apply these laws to simplify expressions before mapping them to gates.
Applications of Logic Gates
- Digital circuits & embedded systems
- ALUs and arithmetic units
- Memory elements (RAM, ROM)
- Signal conditioning and control
- Microcontrollers & processors
From simple door locks to CPUs, gates create deterministic, fast, and scalable digital behavior.
One-Glance Summary Table
| Gate | Symbol | Boolean Expression | Output = 1 When… |
|---|---|---|---|
| AND | ⋅ | A⋅B | Both inputs are 1 |
| OR | + | A+B | Any input is 1 |
| NOT | ¬ | A’ | Input is 0 |
| NAND | ⋅ + ¬ | (A⋅B)’ | Any input is 0 |
| NOR | + + ¬ | (A+B)’ | Both inputs are 0 |
| XOR | ⊕ | A’B+AB’ | Inputs differ |
| XNOR | ⊙ | AB+A’ B’ | Inputs are same |
The approach followed at E Lectures reflects both academic depth and easy-to-understand explanations.
People also ask:
Because any Boolean function can be realized using only NAND or only NOR, enabling complete circuit design from a single gate family.
XOR outputs 1 when inputs are different; XNOR outputs 1 when inputs are the same.
In processors, memory, digital control, communication interfaces, and embedded devices—from appliances to smartphones.
Minor symbol variations exist (¬A vs A‾\overline{A}A), but behavior and truth tables remain identical.
