Boolean Algebra

APA Citation: James, J. (2014, June 07). Boolean algebra explained part-1. Retrieved July 2, 2019, from https://www.youtube.com/watch?v=2zRJ1ShMcgA

Summary:  

Boolean Algebra is centered on three operators, or gates: Not, And and Or gates – uses 1 (true) & 0 (false). 

“Not” gates takes only one input and gives the opposite of what is put in (if 0 is input, 1 is returned, and vice versa).  In Boolean notation this is written A.

Input	Output
1	0
0	1

“And” gates gives one output from two inputs (input 0, 0 -> output 0; input 0,1 -> output 0; input 1, 0-> output 0; input 1, 1 -> output 1).  In Boolean notation this is written Q = A ∙ B. To have an output of 1, both inputs must be 1. Three inputs are allowed and in order to get an output of 1, all three inputs must be 1.  

Input 1	Input 2	Output
1	1	1
1	0	0
0	1	0
0	0	0

“Or” gates can have two or more inputs.  (input 0, 0 -> output 0; input 0, 1 -> output 1; input 1, 0-> output 1; input 1, 1 -> output 1).  In Boolean notation Q = A + B. To have an output of 1, one of the inputs must be a 1. Three inputs are allowed and in order to get an output of 1, only one if the inputs must be 1.

Input 1	Input 2	Output
1	1	1
1	0	1
0	1	1
0	0	0

Things Learned: 

Boolean operators are based on one of two outcomes and they are well defined: yes or no, true or false, on or off.  This can be applied to think logically and make decisions. 

My Question:

This answers my question about mathematical thinking as logic is needed when using the gates to take a limited number of inputs and use them to find the one output desired.