How Can You Simplify Boolean Expressions Using Only NOR Gates?

[benEE2018]

Homework Statement

Hi everyone, i am currently struggling in my digital design and logic class that includes boolean simplifications and whatnot. I seem to understand how to simplify and am able to comprehend how the karnaugh maps work but what i do not understand is for example, on our midterm, how you simplify a boolean expression and draw the logic circuit with only two NOR gates or if he gives u the truth terms (sigma 1.2.3, etc) how to use the kmap and output the function in only nand and nor gates. is there a way to attack these problems?

Homework Equations

an example f(a,b,c,d)= (a exclusive or b)'(c exclusive or d). draw a logic diagram using only two input nor gates to implement the following.

another one
f=wx'+y'z'+w'yz'
using only two level nor gates

i don't need the solutions just a methodical way to approach these types of problems
another

The Attempt at a Solution

i just want to know if there is a certain way i am suppose to be apporaching these kinds of problems

 

[NascentOxygen]

draw a logic diagram using only two input nor gates to implement the following.

I'm speaking before I even look at the question, but I doubt that you are being asked to perform miracles by employing nothing more than a pair of NOR gates for the task.

Most likely this was written as "two-input NOR gates" meaning any number of gates you desire, but where each gate has two inputs only, plus, of course, an output.

Big difference!

 

[NascentOxygen]

Basically, you have to go about replacing whatever logic functions the given expression uses with that of the gates you must implement it with. To do this apply De Morgan's theorem/s where you can replace AND by OR, and vice versa. So you must memorize De Morgan's theorem and know how to apply it. Just memorize one, because the other is easily written by doing a swap of the functions.

I remember like this: "the AND of the inverses = the inverse of the ORs"