PoS Simplification

1
PoS SimplificationDont-Care Condition

• Yahya E. Osais
• COE 200
• Section 03

2
PoS Simplification Procedure

• Mark the empty squares with 0s
• Apply the procedure described previously on the
  cells containing 0s.
• You obtain SoP expression for F
• Complement F
• Take dual complement each literal
• ? You obtain PoS expression for F.

3
Dont-Care Condition

• Incompletely Specified Function
• A function that has unspecified outputs for some
  input combinations.
• An unspecified output is denoted by an X (Dont
  Care Value).
• F X IF
• Input combination never occurs.
• Input occurs but we dont care about the value of
  the output.

4
Dont-Care Condition (contd)

• If you have Xs in the truth table, you should
  mark the appropriate cells in the K-map with Xs.
• X can be 0 or 1
• X is included in an implicant to make it larger
• Simplify the following function
• F(a,b,c,d) ? m (1 , 3 , 7 , 11 , 15)
• d(a,b,c,d) ? m (0 , 2 , 5) ? set of dont-care
  minterms
• When you implement F, the output corresponding to
  a dont-care minterm will be equal to 1 if the
  dont-care minterm is used.