NAND Gate Simulator
Use the free NAND Gate Simulator to test NAND logic instantly. Switch Input A and Input B between 0 and 1 and see the output update immediately. A NAND gate is an AND gate followed by NOT, so its output is 0 only when both inputs are 1.
What Is a NAND Gate?
A NAND gate is a digital logic gate that performs an AND operation and then inverts the AND result. The name NAND comes from the words NOT AND.
For a standard two-input NAND gate, the output is 1 for three of the four possible input combinations. The output becomes 0 only when both Input A and Input B are 1.
NAND Gate Truth Table
| Input A | Input B | AND | NAND Output |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
How to Use the NAND Gate Simulator
Choose either binary 0 or binary 1.
Set the second input to LOW (0) or HIGH (1).
The two inputs first pass through ordinary AND logic.
NAND applies NOT to the AND result, reversing 0 to 1 or 1 to 0.
The final value and HIGH / LOW state are shown instantly.
NAND Gate Input and Output Examples
0 NAND 0
0 AND 0 gives 0. Inverting that result gives 1.
0 NAND 1
0 AND 1 gives 0, so NAND produces 1.
1 NAND 0
1 AND 0 gives 0, which becomes 1 after inversion.
1 NAND 1
1 AND 1 gives 1. NOT changes that result to 0.
Why Does 1 NAND 1 Equal 0?
NAND begins with an AND operation. Both inputs being 1 means the intermediate AND result is 1.
Why Does 0 NAND 0 Equal 1?
The AND result of two zero inputs is 0. NAND then reverses that value.
NOT 0 = 1 Therefore: 0 NAND 0 = 1
NAND Gate Boolean Expression
The standard NAND expression is an AND expression with inversion applied to its result.
| Notation | Expression |
|---|---|
| Word form | A NAND B |
| Expanded form | NOT(A AND B) |
| Boolean form | AND expression with an inversion bar over the result |
NAND Gate vs AND Gate
NAND and AND always produce opposite outputs for the same inputs.
| A | B | AND | NAND |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
Why Is NAND Called a Universal Gate?
NAND is called a universal gate because combinations of NAND gates can reproduce the behavior of NOT, AND, OR, and therefore any Boolean logic function.
This makes NAND particularly important in digital logic design because a complete circuit can theoretically be constructed using only NAND gates.
Creating a NOT Gate with NAND
Connect both NAND inputs to the same signal.
1 NAND 1 = 0 Therefore: A NAND A = NOT A
Creating an AND Gate with NAND
First generate NAND, then invert the NAND output using another NAND configured as a NOT gate.
Creating an OR Gate with NAND
De Morgan’s law allows OR logic to be built entirely from NAND gates.
Y = B NAND B Then NAND those results: Q = X NAND Y Which produces: Q = A OR B
NAND and De Morgan’s Law
One of De Morgan’s identities explains NAND as OR between inverted inputs:
This relationship is useful for transforming logic circuits while preserving the same Boolean behavior.
NAND Gate Symbol
The NAND symbol resembles an AND gate with a small circle at its output. That circle is called an inversion bubble.
The bubble indicates that the AND result is inverted before becoming the final output.
Three-Input NAND Gate
A NAND gate can have more than two inputs. With three inputs, output becomes 0 only when all three inputs are 1.
If any required input is 0, the underlying AND result is 0 and NAND produces 1.
NAND Gates in Memory Circuits
Cross-coupled NAND gates can be used to construct an SR latch, one of the basic building blocks for storing a digital state.
More advanced storage circuits, registers, and sequential systems build on related feedback and gating concepts.
Where Are NAND Gates Used?
Processors
NAND logic can form arithmetic, control, and Boolean circuits inside digital processors.
Memory
NAND-based latch structures and NAND flash technology make the term especially common in storage systems.
Control Circuits
Create inverted conditions and multi-signal control logic.
Logic Synthesis
Complex Boolean functions can be implemented using NAND gates alone.
Embedded Systems
Discrete NAND devices can provide signal control, inversion, gating, and interface logic.
Digital Education
NAND is central to learning Boolean algebra, universal gates, De Morgan’s laws, and circuit design.
NAND Gate vs NOR Gate
NAND
NAND is NOT(A AND B). It produces 0 only when all inputs are 1.
NOR
NOR is NOT(A OR B). It produces 1 only when all inputs are 0.
Both NAND and NOR are universal gates and can be used to construct complete Boolean logic systems.
Important NAND Gate Properties
| Property | Rule |
|---|---|
| Inverse of AND | NAND = NOT(AND) |
| Both inputs 1 | 1 NAND 1 = 0 |
| Any input 0 | Output becomes 1 |
| Self-input | A NAND A = NOT A |
| Universal | NAND gates alone can construct arbitrary Boolean functions |
Common NAND Gate Mistakes
NAND is the inverse of AND, so every AND output must be flipped.
0 AND 0 equals 0, but NAND inverts that value and produces 1.
NAND inverts AND. NOR inverts OR. Their truth tables are different.
NAND can reproduce NOT, AND, OR, and therefore more complex Boolean functions.
Related BinaryCon Tools
NAND Gate Simulator FAQs
What is a NAND gate?
What is 0 NAND 0?
0 NAND 0 = 1.
What is 0 NAND 1?
0 NAND 1 = 1.
What is 1 NAND 0?
1 NAND 0 = 1.
What is 1 NAND 1?
1 NAND 1 = 0. It is the only two-input combination that produces 0.
What is the NAND Boolean expression?
NOT(A AND B).
Why is NAND called NOT AND?
Why is NAND a universal gate?
How do you make NOT using NAND?
A NAND A = NOT A.
Can an AND gate be built using NAND?
Can OR be built using NAND?
What is the difference between NAND and AND?
What is the difference between NAND and NOR?
Can a NAND gate have more than two inputs?
What does the circle on the NAND symbol mean?
Are NAND gates used in memory circuits?
Does this NAND Gate Simulator require registration?
Test NAND Gate Logic Instantly
Switch both inputs between LOW and HIGH, see the NAND output update instantly, study the complete truth table, and learn why NAND is one of the most important universal gates in digital electronics and Boolean logic.