Difference between revisions of "Boolean Algebra"

From TRCCompSci - AQA Computer Science
Jump to: navigation, search
(Commutative Law)
(Commutative Law)
Line 42: Line 42:
 
The Commutative Law is where equations are the same no matter what way around the letters are written. For example
 
The Commutative Law is where equations are the same no matter what way around the letters are written. For example
 
  <nowiki> A + B = B + A </nowiki>
 
  <nowiki> A + B = B + A </nowiki>
 +
or
 +
<nowiki> A . B = B . A </nowiki>
  
 
==Associate Law==
 
==Associate Law==

Revision as of 08:22, 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

The logic gate 'OR' in Boolean algebra is represented by a '+' symbol. For example, if I was to represent "A or B" in Boolean algebra, it would look like this: [math] a+b [/math]

Laws

Commutative Law

The Commutative Law is where equations are the same no matter what way around the letters are written. For example

 A + B = B + A 

or

 A . B = B . A 

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