Question

In some problems involving Boolean expressions, a simpler answer can be obtained using the Karnaugh map of the complement of the expression to be simplified (that is, interchange Is and blanks in the Karnaugh map). The answer is then expressed as the complement of the simplified expression obtained from the Karnaugh map. Use this method to simplify the following Boolean expressions:

(a) xy'z'+x'y'z
(b) xyzw+xy'z'w+xy'z'w'

Answer 1

To simplify the given Boolean expressions using the Karnaugh map complement method, we need to interchange 1s and 0s in the Karnaugh map and find the simplified expression. (a) xy'z' + x'y'z can be simplified to (y'z' + y'z)x'. (b) xyzw + xy'z'w + xy'z'w' can be simplified to (y'z' + yzw + xyzw')x'.

Step-by-step explanation:

The Karnaugh map is a graphical method used to simplify Boolean expressions. To simplify a Boolean expression using the Karnaugh map complement method, we need to interchange 1s and 0s in the Karnaugh map and then find the simplified expression. Let's simplify the given Boolean expressions using this method:

(a) For the expression xy'z' + x'y'z, we need to interchange 1s and 0s in the Karnaugh map, which gives us:

00
11

Now, we can find the simplified expression by grouping the 1s:

xy'z' + x'y'z = (y'z' + y'z)x

Taking the complement, the simplified expression becomes:

(y'z' + y'z)xx

(b) For the expression xyzw + xy'z'w + xy'z'w', the Karnaugh map after interchanging 1s and 0s is:

0101
1000

Grouping the 1s, we get:

xy'z' + xy'zw + xyzw' = (y'z' + yzw + xyzw')x

Taking the complement, the simplified expression becomes:

(y'z' + yzw + xyzw')x'