Made easy test series

Question

Can anyone have some trick to solve this type of questions

Answer 1

For this type of questions you need to manipulate the variables and try to reduce the given function to a boolean expression which is functionally complete.

Absorption Law: a + a’b = a + b (for reference)

Consider option A,

f(x,y,z) = x’ + yz’

Now, substitute y in place of x in the above function i.e.

f(y,y,z) = y’ + yz’ = y’ + z’ = (y.z)’

which is nothing but a nand gate and we know that it is universal gate and hence it is functionally complete. Since the given expression can be reduced down to behave as a nand gate we can implement any other function with it.

option C,

f(x,y,z) = xy’ + x’ + x’z = xy’ + x’(1 + z) = xy’ + x’ = x’ + y’ = (x.y)’ (again a nand gate)

Option B,

f(x,y) = x’ + xy = x’ + y

this is not a standard universal function. Hence not functionally complete.

Hence, correct options (A) & (C).

Comments

Thank you , it is very easy to understand