Difference between revisions of "Boolean Algebra"
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<math> A = A </math> | <math> A = A </math> | ||
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This equation means that the output is determined by the value of A. So if A =0, The output is 0, and vice versa. | 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> | <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. | 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> | <math> A.A = A</math> | ||
+ | |||
The output is determined by A alone in this equation. This can be simplified to just "A". | The output is determined by A alone in this equation. This can be simplified to just "A". | ||
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:
or
this can be done by adding the following around any term you wish to negate.:
<math> \overline{} </math>
is
<math> \overline{a} </math>
is
<math> \overline{\overline{a}+b} </math>.
Contents
Identities
AND Identities
This equation means that the output is determined by the value of A. So if A =0, The output is 0, and vice versa.
Because there is a 0 in this equation, the output of this will always be 0 regardless of the value of A.
The output is determined by A alone in this equation. This can be simplified to just "A".
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:
Laws
Commutative Law
The Commutative Law is where equations are the same no matter what way around the letters are written. For example
or
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: