Difference between revisions of "Boolean Algebra"

From TRCCompSci - AQA Computer Science
Jump to: navigation, search
(OR Identities)
(Commutative Law)
Line 57: Line 57:
 
==Commutative Law==
 
==Commutative Law==
 
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
<math> A+B=B+A </math>
+
<math> A+B = B+A </math>
or
 
<math> A.B=B.A </math>
 
  
 
=Laws=
 
=Laws=

Revision as of 08:37, 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

[math] 0+A = A [/math]

If 0 or A goes in, A is the output

[math] 1+A = 1 [/math]

If 1 or A goes in, 1 is the output

[math] \overline{A}+1=1[/math]

If NOT A or 1 goes in, the output is 1

[math] \overline{A}+A=1[/math]

If NOT A or A goes in, the output is 1

Laws

Commutative Law

The Commutative Law is where equations are the same no matter what way around the letters are written. For example [math] A+B = B+A [/math]

Laws

Associate Law

Distributive Law

The distributive law is these two equations.

[math] A.(B+C) = A.B + A.C [/math]

[math] A+(B.C) = (A+B).(A+C) [/math]

Redundancy Law

[math] \overline{A} = \overline{A} [/math] or [math] \overline{\overline{A}} = A [/math]

Identity Law

[math] A+A = A [/math]

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