# NOR logic

This article is about NOR Logic in the sense of building other logic gates using just NOR gates. For NOR gates, see NOR gate. For NOR in the purely logical sense, see Logical NOR. For logic gates in general, see Logic Gate.
A single NOR gate

Like NAND gates, NOR gates are so-called "universal gates" that can be combined to form any other kind of logic gate. For example, the first embedded system, Apollo Guidance Computer, was built exclusively from NOR gates, about 5,600 in total for the later versions. Today, 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).

## NOR

A NOR gate is logically an inverted OR gate. By itself has the following truth table:

Truth Table
Input A Input B Output Q
0 0 1
0 1 0
1 0 0
1 1 0

## Making other gates by using NOR gates

A NOR gate is a universal gate, meaning that any other gate can be represented as a combination of NOR gates.

### NOT

This is made by joining the inputs of a NOR gate. As a NOR gate is equivalent to an OR gate leading to NOT gate, this automatically sees to the "OR" part of the NOR gate, eliminating it from consideration and leaving only the NOT part.

output= NOT(A+A)
Desired Gate NOR Construction
Truth Table
Input A Output Q
0 1
1 0

### OR

The OR gate is simply a NOR gate followed by another NOR gate.

Output= NOT[NOT(A+B)+NOT(A+B)]
Desired Gate NOR Construction
Truth Table
Input A Input B Output Q
0 0 0
0 1 1
1 0 1
1 1 1

### AND

An AND gate gives a 1 output when both inputs are 1; a NOR gate gives a 1 output only when both inputs are 0. Therefore, an AND gate is made by inverting the inputs to a NOR gate.

Desired Gate NOR Construction
Truth Table
Input A Input B Output Q
0 0 0
0 1 0
1 0 0
1 1 1

### NAND

A NAND gate is made using an AND gate in series with a NOR gate:

Desired Gate NOR Construction
Truth Table
Input A Input B Output Q
0 0 1
0 1 1
1 0 1
1 1 0

### XOR

An XOR gate is made by connecting the output of 3 NOR gates (connected as an AND gate) and the output of a NOR gate to the respective inputs of a NOR gate. This expresses the logical fomula (A AND B) NOR (A NOR B). This construction entails a propagation delay three times that of a single NOR gate.

Desired Gate NOR Construction
Truth Table
Input A Input B Output Q
0 0 0
0 1 1
1 0 1
1 1 0

### XNOR

An XNOR gate can be constructed from four NOR gates implementing the expression "(A NOR N) NOR (B NOR N) where N = A NOR B".This construction has a propagation delay three times that of a single NOR gate, and uses more gates.

Desired XNOR Gate NOR Construction
Truth Table
Input A Input B Output Q
0 0 1
0 1 0
1 0 0
1 1 1