Difference between revisions of "Boolean Algebra"

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(AND Identities)
(OR Identities)
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==OR Identities==
 
==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:
+
The logic gate 'OR' in Boolean algebra is represented by a '+' symbol. The identities for the 'OR' gate in Boolean algebra is as follows:
<math> a+b </math>
+
 
 +
<math> 0+A = A </math>
 +
"If 0 or A go in, A is the output"
 +
 
 +
<math> 1+A = 1 </math>
 +
"If 1 or A is the output, 1 is the output"
 +
 
 +
<math>
  
 
=Laws=
 
=Laws=

Revision as of 08:25, 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. The identities for the 'OR' gate in Boolean algebra is as follows:

[math] 0+A = A [/math] "If 0 or A go in, A is the output"

[math] 1+A = 1 [/math] "If 1 or A is the output, 1 is the output"

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

[math] A.B=B.A [/math]

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