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⚡ Interactive Logic Gate

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.

✓ Interactive Inputs ✓ Instant Output ✓ Truth Table ✓ Universal Gate ✓ Free Unlimited Use
NAND
2-Input NAND Gate
● Live
Input A
0
NAND
NOT(A · B)
Input B
0
Output Q
1
HIGH / TRUE
0 NAND 0 = 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.

Boolean rule: Q = NOT(A AND B) Equivalent idea: NAND = AND followed by NOT

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
Core rule: a two-input NAND gate outputs 0 only for the input combination 1,1.

How to Use the NAND Gate Simulator

Select Input A

Choose either binary 0 or binary 1.

Select Input B

Set the second input to LOW (0) or HIGH (1).

Evaluate the AND result

The two inputs first pass through ordinary AND logic.

Invert the AND output

NAND applies NOT to the AND result, reversing 0 to 1 or 1 to 0.

Read Output Q

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.

1 AND 1 = 1 Then invert: NOT 1 = 0 Therefore: 1 NAND 1 = 0

Why Does 0 NAND 0 Equal 1?

The AND result of two zero inputs is 0. NAND then reverses that value.

0 AND 0 = 0
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
0001
0101
1001
1110

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.

NAND and NOR are both functionally complete, meaning either gate type alone can be combined to implement arbitrary Boolean logic.

Creating a NOT Gate with NAND

Connect both NAND inputs to the same signal.

A NAND A Because: 0 NAND 0 = 1
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.

First: X = A NAND B Then: Q = X NAND X The result is: Q = A AND B

Creating an OR Gate with NAND

De Morgan’s law allows OR logic to be built entirely from NAND gates.

Invert each input: X = A NAND A
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:

NOT(A AND B) = (NOT A) OR (NOT B)

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.

Q = NOT(A AND B AND C) The only LOW combination is: 1 NAND 1 NAND 1 → 0

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.

Latch behavior involves feedback and input-state rules beyond the simple two-input combinational NAND operation shown by this simulator.

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

Using the AND truth table directly

NAND is the inverse of AND, so every AND output must be flipped.

Thinking 0 NAND 0 equals 0

0 AND 0 equals 0, but NAND inverts that value and produces 1.

Thinking NAND is the same as NOR

NAND inverts AND. NOR inverts OR. Their truth tables are different.

Forgetting why NAND is universal

NAND can reproduce NOT, AND, OR, and therefore more complex Boolean functions.

Related BinaryCon Tools

AND Gate Simulator OR Gate Simulator NOT Gate Simulator NOR Gate Simulator XOR Gate Simulator XNOR Gate Simulator Binary AND Calculator Binary NOT Calculator

NAND Gate Simulator FAQs

What is a NAND gate?
A NAND gate performs AND and then inverts the result. NAND means NOT AND.
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?
The expression is NOT(A AND B).
Why is NAND called NOT AND?
Because it first performs AND and then applies NOT to the AND output.
Why is NAND a universal gate?
NAND gates can be combined to reproduce NOT, AND, OR, and any Boolean function constructed from those operations.
How do you make NOT using NAND?
Connect both NAND inputs to the same signal: A NAND A = NOT A.
Can an AND gate be built using NAND?
Yes. NAND the inputs first, then invert that result using a second NAND with its two inputs connected together.
Can OR be built using NAND?
Yes. Invert both inputs using NAND gates and NAND the two inverted signals. This follows De Morgan’s law.
What is the difference between NAND and AND?
Their outputs are always opposite. AND produces 1 for input 11, while NAND produces 0.
What is the difference between NAND and NOR?
NAND is the inverse of AND. NOR is the inverse of OR.
Can a NAND gate have more than two inputs?
Yes. A multi-input NAND gate outputs 0 only when every input equals 1.
What does the circle on the NAND symbol mean?
The small output circle is an inversion bubble showing that the AND result is inverted.
Are NAND gates used in memory circuits?
Yes. NAND gates can form latch circuits, and NAND-based structures are also important in digital storage technologies.
Does this NAND Gate Simulator require registration?
No. You can test all NAND input combinations directly for free.

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.

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