# How do NAND programmers work

## NAND gate

Do you want to know what a NAND gate is? In the following we show you the truth table and the boolean expression.

• Combinations and circuit symbol
in the text
• NAND gate 3 inputs truth table
in the text

### Combinations and circuit symbol

In addition to the simpler logic gates AND, OR and NOT, there are a number of other gates. These are always made up of a combination of the three named. The NAND gate is one of them.

In the German-speaking world, it is also referred to as a not-and-gate and is made up of an and-gate, followed by a not-gate. The NAND gate looks like this in the schematic:

In our example we consider 3 inputs and 1 output X. The point after the AND gate represents the non-function and inverts the output of the gate again.

### NAND gate 3 inputs truth table

Let's take a look at the associated truth table. On the left side we always have all possible combinations of the inputs. In this case we have three: A, B and C. On the right hand side you can see that the result X is always 1, except when all three inputs are 1.

The NAND function thus leads to the opposite result of an AND gate. The Boolean expression for the not-and function is: X is not A and B.

You can also write the boolean expression like this:

Don't get confused by the different types of display! They can all be used interchangeably.

The NAND gate, like the NOR gate, is called a universal logic gate. The reason is that every logical function can be represented with both gates.

You have now got to know the NAND gate and know that you can form all logical functions with it. You can also express the logic functions of the gate in Boolean algebra!