Chapter 2 Digital Logic 2.2.1 Boolean Expression Forms

Chapter 2 : Digital Logic 

2.2.1 : Boolean Expression Forms

by : Muhammad Azmil Bin Ariffin B031210006

Boolean Expression Forms

Sum-Of-Products (SOP);

   

1. Combination of input values that produce 1s is convert into equivalent variables, ANDed together then ORed with other combination variables with the same output.
2. SOP is easier to derive from truth table.

SOP Expression;

Decimal Value	A	B	C	f
0	0	0	0	1
1	0	0	1	0
2	0	1	0	1
3	0	1	1	1
4	1	0	0	0
5	1	0	1	0
6	1	1	0	0
7	1	1	1	1

Products-Of-Sum(POS);

1. Input combinations that produce 0 in sum terms (0Red) variables) are ANDed together.
2. Convert input values that produce 0s into equivalent variables, 0Red the variables, then ANDednwith other ORed forms.
3. Usually use if more 1s produce in output function.

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

Decimal Value	A	B	C	f
0	0	0	0	0
1	0	0	1	0
2	0	1	0	0
3	0	1	1	1
4	1	0	0	1
5	1	0	1	0
6	1	1	0	1
7	1	1	1	1

POS Expression;

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