NOR-NOR logic

Also called: NOR-NOR, NOR-NOR circuit, NOR-NOR implementation, two-level NOR logic

A two-level circuit made only of NOR gates that implements a product of sums. It is an OR-AND circuit with every gate replaced by a NOR.

NOR-NOR logic is the mirror image of nand nand logic. It builds any product of sums expression using only NOR gates, in two levels.

The recipe:

Draw the OR-AND circuit: one OR per sum term, all feeding one AND.
Replace every gate with a NOR.

Why it works, by bubble pushing: add a pair of bubbles to each wire between the levels. Each OR gains an output bubble and becomes a NOR. The AND gains bubbled inputs, and an AND with bubbled inputs is a NOR.

In algebra, for , drawn above:

= by De Morgan's law.

A two-level circuit of NORs therefore naturally gives a product of sums. If you start from a sum of products, convert it to POS first, or use NAND-NAND instead.

As with NAND-NAND, a sum term that is a single literal has no first-level gate, so it must enter the output NOR inverted. For , the output NOR's inputs are and .

Worked example

Example

Y = (A + B')(B + C) with NORs only

Build using only 2-input NORs.

1.
is needed, so gate 1 is a NOR with both inputs tied to B.
2.
Gate 2: NOR(A, ) gives .
3.
Gate 3: NOR(B, C) gives .
4.
Gate 4: NOR of gates 2 and 3 gives .
5.
Check A = 0, B = 1, C = 0: gate 1 = 0, gate 2 = NOR(0, 0) = 1, gate 3 = NOR(1, 0) = 0, gate 4 = NOR(1, 0) = 0. And = 0 · 1 = 0. ✓

Common mistakes

Using NOR-NOR for a sum of products directly. Two levels of NOR give a product of sums.
Reading the output NOR as an OR. With bubbles pushed, it acts as an AND of the sum terms.
Forgetting to invert a single-literal sum term before it enters the output NOR.

Practice NOR-NOR logic

Interactive questions with instant feedback and a worked solution for every wrong answer.

Logic Gates lesson

True or false: a two-level circuit of NOR gates (NORs feeding one output NOR) naturally implements a product of sums.

Boolean Simplification lesson full course

Practice exams

Learn it step by step

NOR-NOR logic is taught in Logic Gates and Boolean Simplification.

Logic Gates →Boolean Simplification →

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