Boolean Algebra
Boolean algebra is used to decide logical statements and draw up truth tables. It uses the rules:
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0 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 1 | 0 |
The operation
is identical to the AND statement in logic, the operation
is identical to the OR statement and the operation
is identical to the NOT statement.
From these simple operations we can build up statements that describe other types of logic operations such as NAND, NOR etc, and very complicated circuits. For each statement we may draw up a truth table. For example
has the truth table below.
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0 | 0 | 1 | 1 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 0 | 1 | 0 |
In addition there are a set of laws which can be applied to expand and simplify Boolean expressions, so that simpler circuits can be designed to produce a desired output.