Implementing a boolean function using two 2X1 multiplexers

  • Thread starter Thread starter bd411
  • Start date Start date
  • Tags Tags
    Function
Click For Summary

Discussion Overview

The discussion revolves around implementing the boolean function F = A'B'C' + AB + AC using two 2X1 multiplexers. Participants explore methods for synthesizing the function, considering the constraints of the problem and the potential use of additional logic components.

Discussion Character

  • Homework-related
  • Debate/contested
  • Exploratory

Main Points Raised

  • Some participants express uncertainty about whether the use of additional logic gates is permitted alongside the multiplexers, suggesting that typically only multiplexers would be used.
  • One participant proposes a synthesis technique involving the use of 2-input multiplexers to implement AND and NOT functions, indicating that any logic function could potentially be constructed using only multiplexers.
  • Another participant shares their observations from the truth table, noting specific conditions under which the output F simplifies based on the values of A and B.
  • There is a mention of the importance of avoiding unnecessarily complex solutions, with participants discussing the need for a methodical approach to the problem.
  • A participant acknowledges the need to focus on the truth table to guide their solution process.
  • One participant cautions against providing direct answers to homework questions, emphasizing adherence to forum rules.

Areas of Agreement / Disagreement

Participants generally agree that the problem may not intend for the use of additional logic gates, but there is no consensus on the optimal approach to implement the function using the specified multiplexers. The discussion remains unresolved regarding the best method to achieve the implementation.

Contextual Notes

Participants express varying levels of confidence in their approaches, and there are references to the truth table without a clear resolution on the mathematical steps involved in synthesizing the function.

bd411
Messages
39
Reaction score
0

Homework Statement


Implement the following function using two 2 X 1 multiplexers.

F = A'B'C' + AB + AC

Where A' = NOT A;
and A = A.


Homework Equations



No equations although knowledge of the workings of the multiplexers is required. The top line on the box labelled MUX is the data select line, and selects one of two (hence 2X1) inputs to appear at the output.


The Attempt at a Solution



I believe I have a solution although pretty much stumbled across it by perseverance. If anyone can tell me a methodical way to determine the solution it would be most appreciated ! Also, I don't know whether my solution is unnecessarily complex ? Any suggestions for simplification are most welcome and appreciated !

Of course, I may be completely wrong, in which case please help me out !
 

Attachments

  • MUX.jpg
    MUX.jpg
    27.2 KB · Views: 1,482
Physics news on Phys.org
bd411 said:

Homework Statement


Implement the following function using two 2 X 1 multiplexers.

F = A'B'C' + AB + AC

Where A' = NOT A;
and A = A.


Homework Equations



No equations although knowledge of the workings of the multiplexers is required. The top line on the box labelled MUX is the data select line, and selects one of two (hence 2X1) inputs to appear at the output.


The Attempt at a Solution



I believe I have a solution although pretty much stumbled across it by perseverance. If anyone can tell me a methodical way to determine the solution it would be most appreciated ! Also, I don't know whether my solution is unnecessarily complex ? Any suggestions for simplification are most welcome and appreciated !

Of course, I may be completely wrong, in which case please help me out !

Are you supposed to use only 2 MUXs and then you can use whatever other logic you want? That seems a bit strange... Usually you would be asked to use only MUXs and no other logic... (but I think 2 MUXs alone wouldn't be enough on this problem...)

As for a general synthesis technique, I can think of one, but I don't know if it's the most optimal one. With the 2-input MUX you can implement an AND function. With a 2-input MUX you can implement a NOT function. And since you can make any logic function you want using only NAND gates, you should be able to make any logic function with only 2-input MUXs...
 
Yea i also don't think they intended for you to use logic gates as you could express the entire function with logic gates.

Heres what i got but I can't say i used any real process i just thought about it long enough.
Looking at the truth table i noticed that when B was 1 F was A. That took care of half the possible inputs of ABC, looking at the cases of B = 0 i noticed when A was 1 F was C and when A was 0 F was C'.

select lines are bottom inputs
 

Attachments

  • boolean.png
    boolean.png
    744 bytes · Views: 1,383
Thanks a lot for the help guys !

Yeah I see what you guys mean ... the question (as it was worded) was:

Implement the function using
(a) one 4 X 1 multiplexer - easy enough
(b) two 2 X 1 multiplexers.

Although it doesn't specifically say that I can't use any other logic, I would have marks deducted for an unnecessarily complex solution.

Thanks a lot, I guess the process is to look long and hard at the truth table then !
 
haxor489 said:
Yea i also don't think they intended for you to use logic gates as you could express the entire function with logic gates.

Heres what i got but I can't say i used any real process i just thought about it long enough.
Looking at the truth table i noticed that when B was 1 F was A. That took care of half the possible inputs of ABC, looking at the cases of B = 0 i noticed when A was 1 F was C and when A was 0 F was C'.

select lines are bottom inputs

Please don't do students' homework for them here on the PF. That's against the PF rules.
 
Sorry Berkeman, didn't know, I'll hint towards solutions next time.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 6 ·
Replies
6
Views
18K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
2
Views
2K