How to Draw Logic Gate Graphs for NOR and XOR Gates

Click For Summary
SUMMARY

This discussion focuses on drawing logic gate graphs for NOR and XOR gates. Participants clarify the output for a NOR gate with inputs A and B, resulting in output C, and for a XOR gate with inputs X and Y, resulting in output Z. Key points include the definition of XOR as "either the one, or the other (but not both)" and the importance of thoroughness in problem-solving to avoid mistakes. The conversation emphasizes the value of confirming answers through multiple methods.

PREREQUISITES
  • Understanding of logic gates, specifically NOR and XOR gates.
  • Familiarity with graphing techniques for logical outputs.
  • Knowledge of Boolean algebra and its applications in digital logic.
  • Experience with problem-solving in a mathematical or engineering context.
NEXT STEPS
  • Study the principles of Boolean algebra to enhance understanding of logic gates.
  • Learn how to graph outputs for various logic gate combinations.
  • Explore the differences between exclusive-OR and inclusive-OR operations.
  • Practice solving logic gate problems using both rigorous and simplified methods.
USEFUL FOR

This discussion is beneficial for students in electrical engineering, computer science, and anyone interested in digital logic design and analysis.

Femme_physics
Gold Member
Messages
2,548
Reaction score
1

Homework Statement



Graphs A and B are entries to a NOR gate with 2 inputs. Draw the output C.

Graphs X and are entries to a XOR gate. Draw the output Z.

Homework Equations



abxy.jpg



The Attempt at a Solution


NOR.jpg



XOR.jpg
 
Physics news on Phys.org
Looks good.
 
I'm afraid you've slipped at ##\overline{x} \cdot y##.

Tip: XOR means "either the one, or the other (but not both)".
 
I like Serena said:
I'm afraid you've slipped at ##\overline{x} \cdot y##.

Tip: XOR means "either the one, or the other (but not both)".

I'm confused...if XOR mean either this or that, how can u draw it on a single graph?

EDIT: nevermind, I think I figured it out
 
Last edited:
You are making heavy work of this, Femme_physics. Would you like to start again?

All you need are 3 graphs: x and y, and a blank one for your answer. https://www.physicsforums.com/images/icons/icon3.gif

Now graph the answer following this EXCLUSIVE-OR rule: where x differs from y, draw
logic level 1. (And if x equals y, draw level 0.)

That's all there is to it. Too easy! :smile:

I'm not sure why your output trails off to the right at logic 1, where x and y are both at 0 https://www.physicsforums.com/images/icons/icon5.gif
 
Last edited by a moderator:
I'm not sure why your output trails off to the right at logic 1, where x and y are both at 0

Oops, you're right, but I think this is my only mistake right?

As far as "heavy work" -- well, I think it has an added value, being more thorough allows you to see the whole picture and revise the issue better.
 
Femme_physics said:
Oops, you're right, but I think this is my only mistake right?
You have made another careless mistake, which will reveal itself.
As far as "heavy work" -- well, I think it has an added value, being more thorough allows you to see the whole picture and revise the issue better.
Exactly right, there is much to be gained by doing it the rigorous way, if only to confirm that the formula jives with the common sense approach. Unfortunately, the more steps you go through, the greater the opportunity to make mistakes. If this were an exam question, I'm sure the time allocation would be for the simple route. It is good to know how to do the task both ways.

If you solve a problem two ways, agreement of answers usually confirms you as being correct. Disagreement can often highlight the error.
 
You have made another careless mistake, which will reveal itself.

Oh yes, I forgot to include that little block in the middle. Thank you :smile:

Exactly right, there is much to be gained by doing it the rigorous way, if only to confirm that the formula jives with the common sense approach. Unfortunately, the more steps you go through, the greater the opportunity to make mistakes. If this were an exam question, I'm sure the time allocation would be for the simple route. It is good to know how to do the task both ways.

If you solve a problem two ways, agreement of answers usually confirms you as being correct. Disagreement can often highlight the error.

Completely agree :approve:
 
  • #10
Congratulations on your 2000th post to physicsforums, Femme_physics!
SUDsB.gif
 
  • #11
Last edited by a moderator:
  • #12
Finally looks right. :wink:
 
  • #13
Thanks :)
 
  • #14
Last edited by a moderator:
  • #15
Femme_physics said:
Trying to get more practice.
Good idea. Don't forget exclusive-OR, too. :cool:
Here A and B are Or Gates, with C being the outcome

X and Y are AND Gates, with Z being the outcome

I drew the graphs of the outcome.

Looks good?
yes​
 
Last edited by a moderator:
  • #16
Thanks NascentOx :)
 

Similar threads

Proving XOR Gate Universality: Elementary Operations & Logical Manipulation
  • · Replies 10 ·
Replies
10
Views
3K
Engineering Combinational Logic Circuits using Logic Gates
  • · Replies 1 ·
Replies
1
Views
2K
Designing an XOR Gate from NOR Gates: Truth Tables and Boolean Algebra
  • · Replies 4 ·
Replies
4
Views
6K
Engineering Circuit Realization of XOR function with Three inputs
  • · Replies 4 ·
Replies
4
Views
5K
Engineering XOR Gate Circuits: Draw Z with Lowest # of 2 Input Gates
  • · Replies 12 ·
Replies
12
Views
3K
Designing a NAND Gate Logic Circuit
  • · Replies 2 ·
Replies
2
Views
2K
Implementing a boolean function using NOR gates
  • · Replies 1 ·
Replies
1
Views
3K
Engineering Write the Boolean expression of a given logic circuit
  • · Replies 2 ·
Replies
2
Views
3K
Designing a 2-bit Comparator with NOR gates
  • · Replies 7 ·
Replies
7
Views
8K
How Can You Simplify Boolean Expressions Using Only NOR Gates?
  • · Replies 2 ·
Replies
2
Views
2K