|
As most people are well
aware, mathematical expressions are used to make computations and other
math problems simpler and smaller. Boolean Algebra is used to do the
same thing, except it does it with logic circuits instead of other
mathematical problems.
The first thing that needs to be known for Boolean algebra is the
meaning of the various signs. There are three of these, all deriving
from the three basic gates. They are AND, OR and NOT.
The AND operation is also known as conjunction. It gives the
product of two binary bits. Using A and B as inputs, it would be
written as AB or sometimes A·B. This of course means that A
is multiplied by B, which is exactly how an AND gate functions.
The OR operation is also known as disjunction. This operation
gives the sum of two binary bits. Again, using A and B as inputs, it
would be written as A + B, which is how an OR gate functions. NOTE, the
"+" does necessarily mean the same thing that it does in normal
mathematics we are all used to. In Boolean algebra, it stands for
OR. For example, 1 + 1 would equal to 1, not 10, the binary
equivalent of two. If either of the inputs is 1, the output is
1. The NOT operation is also known as negation. This operation gives
the opposite of a single term. For example, the negation of A is
written as  .
While the negation of AB would be  .
We can relate the AND, OR and NOT operations to the corresponding gates:
| AND Truth Table |
OR Truth Table |
NOT Truth Table |
| A·B = Y |
A + B = Y |
= Y |
| 0 · 0 = 0 |
0 + 0 = 0 |
0 negated = 1 |
| 0 · 1 = 0 |
0 + 1 = 1 |
| 1 · 0 = 0 |
1 + 0 = 1 |
1 negated = 0 |
| 1 · 1 = 1 |
1 + 1 = 1 |
|
|
43.0% 
