Difference between revisions of "Boolean Algebra"
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==AND 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> A | + | <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 | + | <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 | + | <math> A.\overline{A}=0 </math> |
− | |||
− | |||
==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:
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
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: