Implementing a boolean function using two 2X1 multiplexers

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In summary, the function can be implemented using either one 4 X 1 multiplexer or two 2 X 1 multiplexers. However, an unnecessarily complex solution may be penalized.
  • #1
bd411
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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 !
 

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  • #2
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...
 
  • #3
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
 

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  • #4
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 !
 
  • #5
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.
 
  • #6
Sorry Berkeman, didn't know, I'll hint towards solutions next time.
 

1. How do you implement a boolean function using two 2X1 multiplexers?

To implement a boolean function using two 2X1 multiplexers, you will need to follow these steps:

  • Identify the boolean function and its truth table.
  • Determine the number of inputs and outputs required.
  • Draw a logic diagram using the two 2X1 multiplexers.
  • Assign the inputs and outputs to the corresponding multiplexer pins.
  • Use the select inputs to control which inputs are passed to the output.

2. What is the advantage of using two 2X1 multiplexers to implement a boolean function?

The main advantage of using two 2X1 multiplexers is that they can be cascaded to implement boolean functions with a larger number of inputs. This makes it more cost-effective and space-efficient compared to using larger multiplexers or other logic gates.

3. Can any boolean function be implemented using two 2X1 multiplexers?

Yes, any boolean function can be implemented using two 2X1 multiplexers, as long as it can be expressed in terms of AND, OR, and NOT operations. This is because the two 2X1 multiplexers can be configured to mimic these operations.

4. How do you troubleshoot errors when implementing a boolean function using two 2X1 multiplexers?

If you encounter errors while implementing a boolean function using two 2X1 multiplexers, you can try the following troubleshooting steps:

  • Double-check your logic diagram and make sure the inputs and outputs are assigned correctly.
  • Verify that the truth table for the boolean function is correctly implemented.
  • Check the connections between the multiplexers and other logic gates or components.
  • Test different combinations of inputs to see if the output matches the expected results.
  • If all else fails, consult a colleague or reference material for assistance.

5. Are there any limitations to implementing a boolean function using two 2X1 multiplexers?

One limitation of using two 2X1 multiplexers is that the number of inputs is limited to 4, as each multiplexer has 2 select inputs and each select input can only control 2 inputs. Additionally, as the number of inputs increases, the complexity of the circuit also increases, making it more prone to errors.

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