Logic Design - Combinational Circuits

[Larrytsai]

Homework Statement

Implement the following boolean function with a 4x1 MUX and the minterm number of 2 input external gates. Do not assume that complements are available.

F(A,B,C,D) = (0,1,3,4,8,9,15)What I have done so far is drawn the truth table. At this part since there's only 4 data to be selected, I decided to take AB as my Selectors, and I have divided by truth table into 4 parts (0 to 3), (4 to 7), (8 to 11), (12, 15)
and wrote the outputs.

So far I have written for (0,3) F = C' + D

Can anyone confirm if I am on the right track? I am stuck at the point where I need to implement this without any complements as well as I am not sure if i should be breaking the truth table up into 4 different sections.

 

[KataKoniK]

it is important to approach problems in a systematic and logical manner. In this case, you are on the right track by starting with the truth table and breaking it down into smaller sections. This will make it easier to implement the function with a 4x1 MUX.

However, it is not necessary to use AB as your selectors. You can use any combination of two variables to select the output. In this case, it may be more efficient to use CD as your selectors since the function is already expressed in terms of C and D in the first part of the truth table.

For (0,3), you are correct that the output can be expressed as F = C' + D. To implement this with a 4x1 MUX, you would connect C' to the 0 input, D to the 1 input, and use C and D as your selectors.

For the other parts of the truth table, you can follow a similar approach by expressing the output in terms of the variables and then implementing it with the 4x1 MUX. Remember that you can use AND and OR gates to implement any boolean function, so you may need to use multiple gates to express the output.

In terms of not assuming complements are available, this means that you cannot use NOT gates in your implementation. Instead, you will need to use AND and OR gates to express the output in terms of the variables.

Overall, your approach is correct, but you may want to consider using a different combination of selectors to make the implementation more efficient. Additionally, make sure to carefully consider how to express the output in terms of the variables without using complements. Good luck!