Simple Gates

NOT Gate

AND Gate

OR Gate

NOR Gate

There are three, five or seven simple gates that you need to learn about, depending on how you want to count them (you will see why in a moment). With these simple gates you can build combinations that will implement any digital ­component you can imagine. These gates are going to seem a little dry here, and incredibly simple, but we will see some interesting combinations in the following sections that will make them a lot more inspiring. If you have not done so already, reading How Bits and Bytes Work would be helpful before proceeding.

NOT Gate

The simplest possible gate is called an "inverter," or a NOT gate. It takes one bit as input and produces as output its opposite. The logic table is:

A  Q

0  1

1  0

The NOT gate has one input called A and one output called Q ("Q" is used for the output because if you used "O," you would easily confuse it with zero). The table shows how the gate behaves. When you apply a 0 to A, Q produces a 1. When you apply a 1 to A, Q produces a 0. Simple.

AND Gate

The AND gate performs a logical "and" operation on two inputs, A and B:

A  B Q

0  0  0

0  1  0

1  0  0

1  1  1

The idea behind an AND gate is, "If A AND B are both 1, then Q should be 1." You can see that behavior in the logic table for the gate. You read this table row by row, like this:

A  B Q

0  0  0  If A is 0 AND B is 0, Q is 0.

0  1  0  If A is 0 AND B is 1, Q is 0.

1  0  0  If A is 1 AND B is 0, Q is 0.

1  1  1  If A is 1 AND B is 1, Q is 1.

OR Gate

The next gate is an OR gate. Its basic idea is, "If A is 1 OR B is 1 (or both are 1), then Q is 1."

A  B Q

0  0  0

0  1  1

1  0  1

1  1  1

NAND Gate

Those are the three basic gates (that's one way to count them). It is quite common to recognize two others as well: the NAND and the NOR gate. These two gates are simply combinations of an AND or an OR gate with a NOT gate. If you include these two gates, then the count rises to five. Here's the basic operation of NAND and NOR gates -- you can see they are simply inversions of AND and OR gates:

NOR Gate

A  B Q

0  0  1

0  1  0

1  0  0

1  1  0

NAND Gate

A  B Q

0  0  1

0  1  1

1  0  1

1  1  0

The final two gates that are sometimes added to the list are the XOR and XNOR gates, also known as "exclusive or" and "exclusive nor" gates, respectively. Here are their tables:

XOR Gate

A  B Q

0  0  0

0  1  1

1  0  1

1  1  0

XNOR Gate

A  B Q

0  0  1

0  1  0

1  0  0

1  1  1

XOR Gate

XNOR Gate

The idea behind an XOR gate is, "If either A OR B is 1, but NOT both, Q is 1." The reason why XOR might not be included in a list of gates is because you can implement it easily using the original three gates listed.

If you try all four different patterns for A and B and trace them through the circuit, you will find that Q behaves like an XOR gate. Since there is a well-understood symbol for XOR gates, it is generally easier to think of XOR as a "standard gate" and use it in the same way as AND and OR in circuit diagrams.