Logic Gates
Building Blocks of Digital Systems
What is a Logic Gate?
Definition
A logic gate is an electronic circuit that takes binary inputs (0 or 1) and produces a binary output based on a logical operation.
Binary Representation:
0 = LOW voltage (off, false)
1 = HIGH voltage (on, true)
Gates are the building blocks of all digital systems: processors, memory, controllers, even your smartphone.
In Computer Organization
Logic gates implement the Boolean algebra that CPUs use for decision-making.
Every arithmetic, instruction, and memory control boils down to millions/billions of logic gates.
The Seven Basic Logic Gates
AND Gate
Y = A · B
A
B
Y
0
0
0
0
1
0
1
0
0
1
1
1
Example: Light turns ON only if switch A AND switch B are ON.
OR Gate
Y = A + B
A
B
Y
0
0
0
0
1
1
1
0
1
1
1
1
Example: Door opens if PIN OR fingerprint is correct.
NOT Gate (Inverter)
Y = ¬A
A
Y
0
1
1
0
Example: Alarm sounds if NOT(Door Closed).
NAND Gate (NOT AND)
Y = ¬(A · B)
A
B
Y
0
0
1
0
1
1
1
0
1
1
1
0
Example: Used in memory chips (SRAM, DRAM).
Universal Gate
→ you can build any circuit with NAND alone.
NOR Gate (NOT OR)
Y = ¬(A + B)
A
B
Y
0
0
1
0
1
0
1
0
0
1
1
0
Example: Used in control logic.
Universal Gate
like NAND.
XOR Gate (Exclusive OR)
Y = A ⊕ B
A
B
Y
0
0
0
0
1
1
1
0
1
1
1
0
Example: Used in adders (Sum bit) and parity checkers.
XNOR Gate (Exclusive NOR)
Y = ¬(A ⊕ B)
A
B
Y
0
0
1
0
1
0
1
0
0
1
1
1
Example: Used in equality checkers (A equals B).
How Logic Gates Are Built (Physical Side)
Transistor Implementation
Inside ICs (chips), gates are built using transistors.
Examples:
A NOT gate uses 2 transistors (CMOS: 1 pMOS + 1 nMOS)
A 2-input NAND gate uses 4 transistors
Billions of these transistors make CPUs.
Physical Reality
Logic gates are real hardware components you can touch (on IC chips).
They're not just theoretical concepts but actual electronic circuits that process binary signals using voltage levels.
Where Logic Gates Are Used in Computers
Arithmetic Logic Unit (ALU)
add, subtract, AND, OR, compare → all gates.
The ALU performs all mathematical and logical operations using combinations of logic gates.
Memory
NAND/NOR gates store bits (SRAM, flip-flops).
Memory cells are essentially flip-flops made from logic gates that can store binary values.
Control Unit
Logic gates decode instructions.
The control unit uses logic gates to interpret and execute instructions from memory.
I/O Devices
Keyboards, displays, networking hardware use gate circuits.
Input and output devices rely on logic gates to process and convert signals.
Important Note
Without logic gates, computers cannot process binary data. They are the fundamental building blocks that enable all digital computation.
Gate-Level Minimization (Simplifying Circuits)
Problem:
More gates = more cost, power, delay.
Solution:
Gate-Level Minimization (GLM) using Boolean Algebra and special methods.
Boolean Laws
Simplify equations using algebraic laws.
Example:
F = A·B + A·B' = A
Karnaugh Maps
Graphical grouping method for 3–5 variables.
Visual approach to finding minimal expressions.
Quine-McCluskey
Tabular simplification algorithm (systematic).
Methodical approach for complex functions.
Espresso Algorithm
Computer-aided minimization for big circuits.
Software-based optimization for large designs.
Less Power
Lower Cost
Faster Performance
More Reliable Circuits
Real-Life Example of Gate Usage
Suppose you want a security system:
Door unlocks only if (PIN entered AND fingerprint correct) OR Master Key is used.
Unlock = (PIN · Fingerprint) + MasterKey
PIN
AND
OR
Unlock
Fingerprint
MasterKey
That's how abstract logic becomes real circuits in computers.
Key Takeaways
Logic gates are the fundamental building blocks of all digital systems, implementing Boolean algebra in hardware form.
Basic building blocks of digital systems
Work with binary signals (0/1)
Real hardware (transistors), not just theory
Can minimize circuits to save power, cost, and delay
ALU, memory, control all built from logic gates