Digital doubt:

Question

We can implement every boolean function of $n$ variables using $2^n*1$ MUX or $2^{n-1}*1$ MUX?

Which one is correct ? How?

Answer 1

We can use n-1 selection lines , and using 0,1 and nth variable and its compliment to realize the function So ans is $2^{n-1}:1$

5 variables means a $2^{5} =32 input multiplexer, with inputs 0 through 31. Convert the terms into binary numbers and hold the corresponding inputs high. For B'CE we have:

A B C D E
X 0 1 X 1

This gives us 4 numbers, since we have 2 don't cares. The four numbers are:

00101 = 5
00111 = 7
10101 = 21
10111 = 23

Hold inputs 5, 7, 21, and 23 high.

Comments

I don't understand second part ?

when inverter is available (complement) we can definitely do in $2^{n-1}*1$ mUx. What if complement is not available ?

What if $0$ and $1's$ are not available?