This is needed in order to simplify a Boolean expression based on the specific variables that you are given
In principle it works in the same way as a truth table
They illustrate a table of possible inputs and mapped against the required output.
They are used to simplify a Boolean expression. They work in a similar way to a truth table with patterns within the table in order to simplify it. They illustrate a table of possible inputs mapped against the required output.
The rules of Karnaugh Maps:
- NO zeros are allowed
- no diagonal joining blocks
- Groups should be as large as possible
- Everyone must be within a block - NO loners
- Groups must be formed in 2n (1,2,4,8,etc.)
- Overlapping is allowed
- Wrap arounds are allowed
Rules of Boolean algebra:
¬ (¬ A) = A
Karnaugh Maps:
a^ b v a ^ ¬b
|
A
B
|
A
0
|
A
1
|
|
B 0
|
|
1
|
|
B 1
|
|
1
|
When complexity increases this is how the numbers in the second row of the table will be:
|
00
|
01
|
11
|
10
|
An example of this:
A^B^CvA^¬B^CvA^B^¬C
|
|
AB
00
|
AB
01
|
AB
11
|
AB
10
|
|
C 0
|
|
|
1
|
|
|
C 1
|
|
|
1
|
|
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