Help understanding Boolean Identities

Thread Starter

atrumblood

Joined May 13, 2012
59
I have been teaching my self Boolean Algebra from the AAC E-Book. I just need to clear something up for my self about Boolean Identities.

That something is the Alphanumeric notation that is used, such as A + 0 = A or A + 1 = 1.

I wish to know if I have understood their meaning and usage.


The usage of a Letter is used to represent a changing input.
The usage of a 1 or a 0 is used to represent a static input.

Is this a correct understanding?
 
Last edited:

Papabravo

Joined Feb 24, 2006
15,073
No. The 1 or the 0 is a literal value. You could also call them H and L, or High and Low or True and False. In any case Boolean Algebra, like any other algebra, starts with a set of elements. In the case of Boolean Algebra the set has exactly two elements and you may call or label them anything you wish. They are literal constans in the same way that 3, or 17 or 997 are integer constants.

The letter 'A' is a Boolean variable which may take either of the possible values from the set {0, 1}. Over the set of elements there are operations like 'AND' and 'OR', and 'NOT' which have rules or truth tables which uniquely define the outputs given the values of the inputs.

In any algebra, an identity is a true statement that says the expression on the left has the same value as the expression on the right.

That's in in a nutshell.
 

Thread Starter

atrumblood

Joined May 13, 2012
59
Ok so 1 or 0 mean high or low respectively.
The chosen letter in this case the letter A can be either 1 or 0, high or low.

I appreciate your clarification.
 
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