SOP and POS:
Please follow the procedure:
SOP: (Sum of Product)
1. Find out the correct truth table.
2. Find out rows lead to result of 1.
3. If the input = 1, then write the input; if the input = 0, write the input’s
complement. (i.e. input is A and B, if A = 0, B = 1, then we write A’B). Each row
should be written in a form of product.
4. Add all the products.
PLEASE READ
POS: (Product of Sums)
CAREFULLY!!!!!
1. Find out the correct truth table.
!
2. Find out rows lead to result of 0.
3. If the input = 0, then write the input; if the input = 1, write the input’s
complement. (i.e. input is A and B, if A = 1, B = 0, then we write AB’). Each row
should be written in a form of addition.
4. Multiply all the sums.
Examples:
The Truth TABLE:
A
B
F
0
0
0
0
1
0
1
0
0
1
1
1
SOP: follow the steps,
Since there is only one row leads to F = 1. The last row: A = 1, B = 1, F = 1.
Thus, apply the rules listed above, IF INPUT=1, WRITE THE INPUT, IF INPUT=0, WRITE
THE INPUT’S COMPLEMENT.
We have: F=AB
POS: follow the steps,
Since there are three row lead to F = 0,
Apply the rules listed above, IF INPUT=1, WRITE THE INPUT’S COMPLEMENT, IF
INPUT=0, WRITE THE INPUT.
We have: F=(A+B)(A+B’)(A’+B)=(AA+BA+AB’+BB’)(A’+B)=(A+A+0)(A’+B)=AA’+AB=AB
Thus, POS = SOP.