Question

Using DeMorgan's Law, write an expression for the complement of F if

F(w, x, y, z) = xz'(x'yz + x) + y(w'z + x').

Answer 1

To write an expression for the complement of F using DeMorgan's Law, we apply the law to invert the operations in the given Boolean function. Each sum becomes a product and vice versa, and each variable and its complement are flipped.

Step-by-step explanation:

The question involves using DeMorgan's Law to find the complement of a Boolean function F(w, x, y, z). According to DeMorgan's Law, the complement of a product of variables is equal to the sum of the compliments of the variables and vice versa. Applying this to the given function F(w, x, y, z) = xz'(x'yz + x) + y(w'z + x') and finding its complement involves the following steps:

1. Apply DeMorgan's Law to the outermost level: F'(w, x, y, z) = (xz'(x'yz + x) + y(w'z + x'))'.
2. Expand the complement over the sum: F'(w, x, y, z) = (xz'(x'yz + x))' (y(w'z + x'))'.
3. Apply DeMorgan's Law to each component: F'(w, x, y, z) = (x' + (z'(x'yz + x))') (y' + (w'z + x'))').
4. Simplify then the inner term using DeMorgan's Law again: F'(w, x, y, z) = (x' + (z + x' + y' + z')) (y' + (w + z' + x)).
5. Continue simplification until complete expression for F' is obtained.