Given a function with 4inputs, F(A,B,C,D) and a 8:1 multiplexer with 3 input selectors, I know I can sometimes have the whole function fitted onto the multiplexer without have any single complement literals.

But I usually do it through trial and error method by listing the entire truth table arranging the columns with A, B, C ,D and match with the result of the function F for ABC as selector inputs. Then if I realise that ABC will make D as one of the complement literals for the multiplexer input, I will need to rearrange the truth table all over again with say A,B,D,C to re-match with the result of the function F with ABD as the selector inputs this time. Then again, if it requires complement literals of C for the multiplexer input, I will need to rearrange the columns and draw the whole truthtable again.

This method is very very time consuming. Is there a better method to do this?

Thanks!

 

I believe can't always do this.

For example, take the XOR function of A and B. No matter how you will arrange them, you will need the variable in the first input of the 2-to-1 MUX and its complement on the other.

I don't know any algorithmic way that you can find the cases that suit you. Maybe you could do the following to facilitate the process:
Create an Excel document and fill your truth table. If you have the variables A, B, C and D, sort the table first by A then by B and so on. Don't sort it by the output. That will create the normal binary count sorting and lets you find the inputs of the MUX referred to D.
But if you change the sorting order you can instantly re-arrange your table and see if another variable can be a more convenient input for your MUX.

 

Thanks Georacer for the tip! I actually used Excel to do this when at home too. In Excel, I could highlight the rows and column and then sort them by order. But I can't do use Excel to help me during the exam.
And it will be terribly time consuming too if I do this manually in the exam.
hmm..

 

I don't think it will be a problem in the exams if you have a couple more NOT gates. Remember: In real life, they come in packs of 6 in a single IC. Use one gate and you get 5 more for free.

 

yea the "NOT" gates will help a lot. But the usual exam questions I've seen so far state that no additional logic gates and complement literals are allowed. It's kinda sick. It just want us to kill some time going through the trial and error process. lol

 

Yeah, I hate out of reality exam questions too...