Any gate can be built from NAND or NOR gates
As well as making a NOT gate, NAND or NOR gates can be combined to create any type of gate! This enables a circuit to be built from just one type of gate, either NAND or NOR. For example an AND gate is a NAND gate then a NOT gate (to undo the inverting function). Note that AND and OR gates cannot be used to create other gates because they lack the inverting (NOT) function.
To change the type of gate, such as changing OR to AND, you must do three things:
- Invert (NOT) each input.
- Change the gate type (OR to AND, or AND to OR)
- Invert (NOT) the output.
For example an OR gate can be built from NOTed inputs fed into a NAND (AND + NOT) gate.
NAND gate equivalents
The table below shows the NAND gate equivalents of NOT, AND, OR and NOR gates:
| Gate | Equivalent in NAND gates |
| NOT |  |  |
| AND |  |  |
| OR |  |  |
| NOR |  |  |
Substituting gates in an example logic system
The original system has 3 different gates: NOR, AND and OR. This requires three ICs (one for each type of gate).
To re-design this system using NAND gates only begin by replacing each gate with its NAND gate equivalent, as shown in the diagram below.
Then simplify the system by deleting adjacent pairs of NOT gates (marked
X above). This can be done because the second NOT gate cancels the action of the first.
The final system is shown on the right. It has five NAND gates and requires two ICs (with four gates on each IC). This is better than the original system which required three ICs (one for each type of gate).
Substituting NAND (or NOR) gates does not always increase the number of gates, but when it does (as in this example) the increase is usually only one or two gates. The real benefit is reducing the number of ICs required by using just one type of gate.
Moderation Team
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