# 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
16,120
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
20,600
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?

#### RBR1317

Joined Nov 13, 2010
712
How do I make the nor gates function as two or gates and an and? Just invert everything?
Yes, by using negative logic. An OR gate with negated output is the same as an AND gate with negated inputs.

#### WBahn

Joined Mar 31, 2012
29,494
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?