Fundamental Digital Electronics/NAND Logic

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Logic NAND[edit]

NAND gates are one of the two basic logic gates (the other being NOR logic) from which any other logic gates can be built. Due to this property, NAND and NOR gates are sometimes called "universal gates". However, modern integrated circuits are not constructed exclusively from a single type of gate. Instead, EDA tools are used to convert the description of a logical circuit to a netlist of complex gates (standard cells) or transistors (full custom approach).

Combined Gates[edit]

NOT[edit]

A NOT gate is made by joining the inputs of a NAND gate. Since a NAND gate is equivalent to an AND gate followed by a NOT gate, joining the inputs of a NAND gate leaves only the NOT part.

Desired Gate NAND Construction
NOT ANSI Labelled.svg NOT from NAND.svg
Truth Table
Input A Output Q
0 1
1 0

AND[edit]

An AND gate is made by following a NAND gate with a NOT gate as shown below. This gives a NOT NAND, i.e. AND.

Desired Gate NAND Construction
AND ANSI Labelled.svg AND from NAND.svg
Truth Table
Input A Input B Output Q
0 0 0
0 1 0
1 0 0
1 1 1

OR[edit]

If the truth table for a NAND gate is examined or by applying De Morgan's Laws, it can be seen that if any of the inputs are 0, then the output will be 1. However to be an OR gate, if any input is 1, the output must also be 1. Therefore, if the inputs are inverted, any high input will trigger a high output.

Desired Gate NAND Construction
OR ANSI Labelled.svg OR from NAND.svg
Truth Table
Input A Input B Output Q
0 0 0
0 1 1
1 0 1
1 1 1

NOR[edit]

A NOR gate is simply an OR gate with an inverted output:

Desired Gate NAND Construction
NOR ANSI Labelled.svg NOR from NAND.svg
Truth Table
Input A Input B Output Q
0 0 1
0 1 0
1 0 0
1 1 0

XOR[edit]

An XOR gate is constructed similarly to an OR gate, except with an additional NAND gate inserted such that if both inputs are high, the inputs to the final NAND gate will also be high, and the output will be low. This effectively represents the formula: "(A NAND (A NAND B)) NAND (B NAND (A NAND B))".

Desired Gate NAND Construction
XOR ANSI Labelled.svg XOR from NAND.svg
Truth Table
Input A Input B Output Q
0 0 0
0 1 1
1 0 1
1 1 0

XNOR[edit]

An XNOR gate is simply an XOR gate with an inverted output:

Desired Gate NAND Construction
XNOR ANSI Labelled.svg XNOR from NAND.svg
Truth Table
Input A Input B Output Q
0 0 1
0 1 0
1 0 0
1 1 1

External links[edit]