# Two level Nor gate implementation

#### Tom Nelson

Joined Oct 27, 2015
3
I am supposed to simplify the following function and implement a two level nor gate circuit:
f(w,x,y,z) = wx'+y'z'+w'yz'

I made a k-map, and the POS form as follows: (w+z')*(x'+z')

A little confused on how to implement in terms of nor now? How do I make the nor gates function as two or gates and an and? Just invert everything?

#### dl324

Joined Mar 30, 2015
14,676
Welcome to AAC!

It would be easier to read your post if you used all caps for the gates:
How do I make the nor gates function as two or gates and an and?
How do I make the NOR gates function as two OR gates and an AND?

#### Tom Nelson

Joined Oct 27, 2015
3
Thank you, I'm going to look over it some more and repost the question with more details later.

#### Papabravo

Joined Feb 24, 2006
18,783
If you think of what a NOR gate and it's DeMorgan equivalent do in terms of signal levels it may become clear to you. The following two statement implement the exact same logic function:
1. A HIGH OR a HIGH is a LOW (Basic Definition of a NOR function)
2. A LOW AND a LOW is a HIGH (DeMorgan equivalent of a NOR gate)
Does that help?

#### WBahn

Joined Mar 31, 2012
26,416
I am supposed to simplify the following function and implement a two level nor gate circuit:
f(w,x,y,z) = wx'+y'z'+w'yz'

I made a k-map, and the POS form as follows: (w+z')*(x'+z')

A little confused on how to implement in terms of nor now? How do I make the nor gates function as two or gates and an and? Just invert everything?
The key is to apply DeMorgan's Theorem.

It is probably easiest to do graphically (what I call "bubble logic"), but can be done with Boolean Algebra as well.

For instance, if you have A*B and apply DeMorgan's, you have (A' + B')'

You should be able to recognize this as A' NOR B'. If A and B are the OR of two terms, what do you have?