We can extend the relationship between max-terms and min-terms to include SOP (Sum of
Products) and Products of Sum (POS):
∏ =∑ ∑ =∏
= =
and
Mi mi and Mi mi
Example:
Write the F(A,B,C)= ∏ )6,5,3,0( in the compact min-term form.
We know that ∑ =∏ Therefore
F AB,,( C)=∑ )6,5,3,0( =∏ )6,5,3,0( =(A+B+C).(A+B+C).(A+B+C).(A+B+C)
Since these terms are the 0’s of the function, if we write the Min-terms that are not present then
we will have the 1’s of the function:
F AB,,( C)=∑ )7,4,2,1( =AB.. C+AB.. C+AB.. C+AB.. C Example
Use only NAND gates to implement f(a 2 , a 1 , a 0 ) = a 2 .a 1 .a 0 + a 2 .a 1
’
.a 0
’
+a 2
’
.a 1
’
.a 0
Solution: Example
Use only NOR gates to implement f(a 2 , a 1 , a 0 ) = (a 2 ’+a 1 +a 0 ’) + (a 2 ’+a 1 ’+a 0 ) + (a 2 ’+a 1 +a 0 )
Solution: