00:01
Hello students, here we have to design a combinational circuit using decoders and external gates for the given boolean functions.
00:09
So here the given boolean functions are f1 equal to x prime y z prime plus xz and f2 is x y prime z prime plus x bar y and f3 is x prime y prime z prime plus xy.
00:30
So first let's take the first boolean function f1 that is equal to x prime y z prime plus xz.
00:40
Now what i am doing is here the first term contains all the variables x y z and here z is missing.
00:49
So in this case i can write x y into z plus z bar.
00:54
We know that z plus z bar will reduce the expression to 1.
00:59
So the term will remain the same that is x y.
01:02
Now we can write x prime y z bar plus multiplying this x y z plus x y z prime.
01:14
Now these are the min terms.
01:16
I can express this expression as a sum of min terms.
01:19
So that is summation of so this is 0 1 0.
01:24
So 0 1 0 means it is 2 and 1 1 1.
01:29
So this is 7 and this is 1 1 0 that is 5.
01:36
So f1 can be expressed as a sum of min terms like this.
01:41
That is summation of 2 7 5.
01:43
And now taking the second expression which is x y prime z prime plus x prime y.
01:51
Here also z is missing.
01:55
So i am adding z plus z bar.
01:58
So x y prime z prime plus x bar y z plus z bar.
02:05
And this will give x y prime z prime plus x bar y z plus x bar y z bar.
02:14
Now if i express them as a sum of min terms we get f2 is equal to summation over this is 1 0 0 that means this is 4 comma 0 1 1 that means 3 and 1 0 1 0.
02:31
This is 2.
02:33
So this is expressed as a sum of 4 comma 3 comma 2.
02:37
And moving to the next boolean function that is f3.
02:43
So f3 is equal to x prime y prime z prime plus x y.
02:50
In this case also the z variable is missing.
02:53
So we can write x prime y prime z prime plus x y into z plus z prime.
03:00
This gives x prime y prime z prime plus x y z plus x y z prime...