## NAND Gate

A **NAND gate** is also called a universal gate. This means that any other gate can be represented as a combination of these gates.

Theoretically, a two-input NAND gate can be implemented by cascading a two-input AND gate and a NOT gate (or inverter gate). See the figure below.

As in the case of the two-input AND gate, the same analysis can be done for the 3-input or more AND gates. As you can see, the X output is “0” only if all inputs are “1”.

## NAND gate truth tables

Note: An interesting case of this type of gate. Like the NOT gate, the output X of the first and last row of the **truth table** has the opposite value of the inputs. In other words: A NAND logic gate can be used to obtain the behavior of a NOT gate.

Although a NAND gate appears to be the combination of two gates (an **AND gate** and a **NOT gate**), it is not. In fact, the NAND logic gate is not built by cascading an AND gate and a NOT gate, but has an independent design.

We can create a NOT gate using a NAND gate. We do this by connecting the inputs of the gate, as shown in the next figure.

Analyzing the truth table of a two-input NAND gate, we see that there are only two cases:

- When A = B = 0, I = 1
- When A = B = 1, I = 0

We can create a logic **OR gate** using NAND gates. We do this by connecting the inputs of the gate, as shown in the next figure.

In the same way, it is possible to create a **NOR gate** by placing a NAND gate at the output of the OR gate equivalent below.

TTL SN7400N – Quad NAND Gate Integrated Circuit

You may want to know **how to make NAND gate with transistors**

### More Digital Tutorials

- What is the difference between Analog & Digital?
- What is a logic circuit?
- Digital logic levels (high, low, 1, 0)
- The truth table
- Boolean algebra
- Karnaugh Map (K-map)
- Binary number system
- Hexadecimal numbering system
- BCD code – binary coded decimal
- Gray code – Gray code table
- Aiken code – Excess 3 code
- AND gate
- NAND gate
- OR gate
- NOR gate
- NOT gate
- XOR gate
- How to build a NAND gate with transistors & diodes?
- OR & AND logic gates made with diodes
- The combinational circuit
- The sequential circuit
- JK Flip-Flop
- What is a binary decoder?