Basic Gates

The NAND Gate

The NAND logic gate is a fundamental building block of computers.

NAND ANSI Labelled

The output (Q) is only off when both inputs (A and B) are on.  This can be expressed using the following truth table.

INPUT OUTPUT
A B A NAND B
0 0 1
0 1 1
1 0 1
1 1 0

STOP RIGHT HERE:  I know, we’ve only just begun.  This gate is so fundamental to understanding the rest of this text that you need to be able to look the values of the inputs of this gate and immediately see the value of the output.  Create 4 flashcards. On each one draw a NAND gate with one of the 4 possible input combinations and on the back draw the output value.  Study these flashcards until you’ve committed them to memory.

The NOT Gate

The NOT gate can be constructed using a NAND gate by connecting both inputs of the NAND gate to a single input as shown below.

NOT from NAND

Since the NOT is just a NAND gate but with fewer input combinations (both on or both off), the truth table for the NOT gate consists of just two rows from the truth table for the NAND gate.

INPUT OUTPUT
A NOT A
0 1
1 0

The NOT gate is usually drawn, not using a NAND gate, but as shown below.

NOT ANSI Labelled

The AND Gate

An AND gate can be constructed using two NAND gates.

AND from NAND

Notice that the second NAND gate is a NOT gate.  Thus, the output of the AND gate simply inverts the output of the first NAND gate.  Here the output is on only if both input are on.

INPUT OUTPUT
A B A AND B
0 0 0
0 1 0
1 0 0
1 1 1

The AND gate too has its own symbol:

AND ANSI

Notice that it is similar to a NAND gate, just without the small circle at the tip of the D curve.

The OR Gate

The OR gate can also be constructed using NAND gates and NOT gates.

OR using NAND

The truth table follows:

INPUT OUTPUT
A B A OR B
0 0 0
0 1 1
1 0 1
1 1 1

The symbol for the OR gate is below.

OR ANSI Labelled

The XOR Gate

The last gate that we’ll need is the XOR gate. It too can be constructed with only NAND gates.

XOR from NAND

The XOR’s output is 1 if only one of the inputs is 1, otherwise the output is 0 as shown in the truth table.

INPUT OUTPUT
A B A XOR B
0 0 0
0 1 1
1 0 1
1 1 0

The symbol used for the XOR gate is below.

XOR ANSI

Alternate AND, OR and XOR Gate Construction

Below is a diagram showing the NOT, AND, OR and XOR gates. These are equivalent to the above constructions.