DIGITAL LOGIC (PART III)

This is the last part for this topic. Hope this part can help you to solve you problem and understand more about Digital logic,,,have funnnnnn...

4.7 LAW OF BOOLEAN ALGEBRA

• This law are use to simplify the Boolean expression.

Examples:

1. Simplify the expression below

F = (A+B) . (A+ C)

   = AA + AC + AB + BC

   = A + AC + AB + BC

   = A(1+C) + AB + BC

   = A + AB + BC

   = A(1 + B) + BC

   = A.1 + BC

   = A + BC

2. Simplify the expression using Boolean law

F = WX + XY + X'Z' + WY'Z'

   = WX + XY + X'Z' + WY'Z'X + WY'Z'X'

   = WX(1 + Y'Z') + XY + X'Z'(1 + WY')

   = WX + XY + X'Z

4.8 KARNAUGH MAP

• Provides a systematic method for simplifying Boolean expressions and produce the simplest SOP or POS expression
• This method converts the truth table information into a two-dimensional map. Its then convert’s area of 1’s on the map into groups that give the simplest expression.

Step 1: Transfer the output into Karnaugh map following the figure above

Step 2: Group the 1s output

Step 3: Convert the maps into expression

The expression is:

POS = A' + B

by nadhiah amira nordin

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