Difference between revisions of "Boolean Algebra"

From TRCCompSci - AQA Computer Science
Jump to: navigation, search
(AND Identities)
(AND Identities)
Line 31: Line 31:
 
<math> \overline{A.B} </math>
 
<math> \overline{A.B} </math>
  
This expression means " NOT A AND B = 1".
+
The line above the equation means "NOT", therefore this expression means " NOT A AND B = 1".
  
 
==OR Identities==
 
==OR Identities==

Revision as of 09:17, 8 May 2018

Any equation must be within the <math> </math> tags. For Boolean alegbra the main issue is how to negate a term like:

[math] \overline{a}[/math] or [math] \overline{\overline{a}+b}[/math]

this can be done by adding the following around any term you wish to negate.:

<math> \overline{} </math>  

[math] \overline{a}[/math]

is

 <math> \overline{a} </math>

[math] \overline{\overline{a}+b}[/math]

is

 <math> \overline{\overline{a}+b} </math>.

Identities

AND Identities

The logic gate AND is represented by the "." symbol. Some examples of an equation containing this operation is:

[math] A.B [/math]

This expression means "A AND B = 1".

[math] \overline{A.B} [/math]

The line above the equation means "NOT", therefore this expression means " NOT A AND B = 1".

OR Identities

Laws

Commutative Law

Associate Law

Distributive Law

Redundancy Law

Identity Law

Negation Law

Equations

Solving equations is a matter of applying the laws of boolean algrebra, followed by any of the identities you can find:

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7