Question
Asked Oct 22, 2019
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Write a simplified expression for the Boolean function defined by each of the following Kmaps.

zA
00
10
01
11
1
1
0
0
0
b)
yz
01
00
11
10
x
1
0
0
1
0
0
0
1
1
c)
yz
00
01
11
10
0
1
0
0
1
1
1
OO
O
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zA 00 10 01 11 1 1 0 0 0 b) yz 01 00 11 10 x 1 0 0 1 0 0 0 1 1 c) yz 00 01 11 10 0 1 0 0 1 1 1 OO O

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Expert Answer

Step 1

K-map stands for Karnaugh map that provides a way of grouping the expression together on the basis of some common factors and eliminating those variables which are unwanted. For the given k- maps, Boolean expressions are formed using the concept of min terms (with result value 1) for sum of product. To find the Boolean expression of k map, all the 1’s are combined in a way to enclose maximum numbers of adjacent squares. Then, the expressions for the enclose terms are written. Here 1 denotes true and 0 denotes false.

Step 2

(a)

The given k map will form squares with maximum number of 1’s in it as shown below.

For each square, write the expression for the terms. The expression is formed as:

  • For the square with two terms, the expression produced is Y’Z’.
  • For the square enclosing four terms, the expression produced is X’.

The boolean expression for given K-map is X’+Y’Z’.

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YZ 00 01 11 10 1 1 1 0 0 0

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Step 3

(b)

The k map will form squares with maximum number of 1’s included in it as shown below.

For each square, write the expression for the terms. Here 1 denotes true and 0 denotes false. The expression is formed as:

  • For the first square, the expression produced is Y’...
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YZ 00 01 11 10 0 0 1 0 0 0

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Computer Science

Boolean Logic

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