Sum-Of-Products & Product-Of-Sums

A Boolean algebra is the combination of variables and operators. 
Typically, it has one or more inputs to produce an output in the range of 0 or 1. 
The compliment of a variable is shown by a bar over a letter.

 

Comparison

SOP	POS
Steps:  1. Combination of input                   values that produces 1s              2. ANDed the input values                  together              3. ORed the values	Steps:  1. Convert input values that                  produce 0s into equivalent                  variables              2. ORed the input values                   together              3. ANDed the values.
Used when more 0s produced in output function	Used when more 1s produced in output function
Expression : F = (A’BC)+(AB’C)+(ABC’)	Expression : F = (A’+B+C)(A+B’+C)                                (A+B+C’)

Example

INPUTS		OUTPUTS
A	B	F	G
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

Sum-of-product

F = (A’ ⋅ B) + (A ⋅ B’)

G = (A ⋅ B)

Product-of-sum

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