Karnaugh Maps-數位邏輯設計筆記

一定愛配王俊堯教授開放課程食用:課程連結

Karnaugh Maps

Minimum Forms of Switching Functions

What is Minimum Forms?

• SOP: Minimum number of terms and literals.
• POS: Minimum number of factors and literals.

What is Karnaugh Map(K-Map)?

• A method to simplify boolean functions.
• For faster, simpler and optimum solutions.

2 and 3 Variables K-Maps

How to solve such problems?

• From Minterm's Perspective:
  1. Fill in the form of K-Map.
  2. Select the terms with the result of 1.

     • Every "1" must be covered.

     • The amount of the terms you select must be .

     • The terms you select must be adjacent to each other.

       

     • Bigger the circles are, simpler the result is.

  3. Ignore the literals with different inputs.
  4. Add ' appropriately and write down the terms.
  5. Done! ### Examples

4 Variables K-Maps

Examples

Minimum Forms with Essential Prime Implicants

Implicants

• Implicant

  • Single element of the ON-SET or any group of elements that can be combined together in a K-Map.

• Prime Implicant

  • Implicant that cannot be combined with another implicant to eliminate a term.

• Essential Prime Implicant

  • If an element of the ON-SET is covered by a single prime implicant, the prime implicant is essential prime implicant.

• 白話文

  

How?

1. Expand implicates into prime implicants.
2. Cover the ON-SET with as few prime implicants as possible.

Exmaples

5 Variables K-Map

Example