Difference between revisions of "Boolean Algebra"

From TRCCompSci - AQA Computer Science
Jump to: navigation, search
(Commutative Law)
(AND Identities)
Line 23: Line 23:
 
==AND Identities==
 
==AND Identities==
  
The logic gate AND is represented by the "." symbol. Some examples of an equation containing this operation is:
+
<math> A = A </math>
 +
This equation means that the output is determined by the value of A. So if A =0, The output is 0, and vice versa.
  
<math> A.B </math>
+
<math> 0.A = 0 </math>
 +
Because there is a 0 in this equation, the output of this will always be 0 regardless of the value of A.
  
This expression means "A AND B = 1".
+
<math> A.A = A</math>
 +
The output is determined by A alone in this equation. This can be simplified to just "A".
  
<math> \overline{A.B} </math>
+
<math> A.\overline{A}=0 </math>
 
 
The line above the equation means "NOT", therefore this expression means " NOT A AND B = 1".
 
  
 
==OR Identities==
 
==OR Identities==

Revision as of 08:24, 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

[math] A = A [/math] This equation means that the output is determined by the value of A. So if A =0, The output is 0, and vice versa.

[math] 0.A = 0 [/math] Because there is a 0 in this equation, the output of this will always be 0 regardless of the value of A.

[math] A.A = A[/math] The output is determined by A alone in this equation. This can be simplified to just "A".

[math] A.\overline{A}=0 [/math]

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