Digital Electronics/Logic NOR

Logic NOR

NOR gates are one of the two basic logic gates (the other being NAND gates) from which any other logic gates can be built. Due to this property, NOR and NAND 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).

Combinational Gates

NOT

A NOT gate is made by joining the inputs of a NOR gate. Since a NOR gate is equivalent to an OR gate followed by a NOT gate, joining the inputs of a NOR gate leaves only the NOT part.

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

AND

If the truth table for a NOR 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 AND gate, only when both inputs are 1, the output is 1. Therefore, if the inputs are inverted, both high inputs will trigger a high output.

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

OR

An OR gate is simple a NOR gate with an inverted output (a NOT gate). The NOT gate is simply a NOR gate with its inputs tied together. Therefore a cascade of two NOR gates, the second one with its inputs connected together will result in an OR gate.

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

NAND

A NAND gate can be implemented by inverting the output of an AND 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 constructed using five NOR gates. Three of the gates are connected in an AND topology. A logical expression for this arrangement is ((A AND B) NOR (A NOR B)).

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 is made by connecting four NOR gates as shown below. This effectively represents the formula: (A NOR (A NOR B)) NOR (B NOR (A NOR B)).

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

Reference

• Floyd, Thomas, L. (1997), Digital Fundamentals (6th ed.), Englewood Cliffs, NJ: Prentice-Hall, ISBN 0133984885.