  Digital Teaching Aid (DED Philippinen, 86 p.)  Karnaugh Mapping - Lesson 4  Lesson Plan  (introduction...) Introduction Karnaugh map Truth table to Karnaugh map Pairs, Quads, and Octets Overlapping and Rolling

Pairs Fig. 4-4: Four variable simplification

As you see in Fig. 4-4, only one variable goes from uncomplement to complement. Whenever this happens, you can eliminate the variable that changes form.

 Proof:  X = A B C

Ex: Fig. 4-5: Pairs

Whenever you see a pair first encircle it and then simplify to get the simplified Boolean expression:  Quad: A group of 4 one's that are horizontally or vertically adjacent. End to end or in form of a square.

A quad eliminates two variables and their complements.

 Proof: (two pairs) X = A B (C + C) X = A B

Encircle the quad and step through the different one's in the quad and determine which two variables go from complement to uncomplement (or vs), these are the variables that drop out.

Ex: The variables B and D can be eliminated. So we get the following equation:

X = A C

Octet Fig. 4-8: Octet

An octet eliminates three variables and their complements.

 Proof: (two quads) X = A (C + C) X = A

Karnaugh Simplifications

Process:

1. Draw the Karnaugh map
2. Look for octets and encircle them.
3. Look for quads and encircle them.
4. Look for pairs and encircle them.
5. Simplify and write down the equation.

Ex: Fig. 4-9: Karnaugh map 