Question

design full adder using 4:1 mux

Answer 1

sol:

Basically to implement a full adder,two 4:1 mux is needed.

Let's start from the beginning.

To implement full adder,first it is required to know the expression for sum and carry.

Here is the expression

Now it is required to put the expression of sum and carry inside a MUX Tree.

For mux tree calculation let's consider the following parameters for MUX.

I(0) to I(3) are the required inputs.

From the above calculation B and C are taken as select lines(taken from the above truth table of Full adder).

And the calculation is done on the A input.

Now from the above diagram the conclusion can be drawn:-

For Sum the SOP form has been rounded off with circles which are(1,2,4,7) and correspondingly either A or Abar is selected depending on the rounding of the number at which it comes.

If any certain pair doesn't match any 0 will appear but in sum expression there is none but in carry expression there is one zero term.

Similarly on the same approach,the carry can also be calculated.

Now putting all these in the circuit it looks like:-

Finally the sum and carry can be taken out as output.