Difference between revisions of "User:HelpJazz/workspace"
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==Three Basic Operations== | ==Three Basic Operations== | ||
| − | The three basic operations of boolean algebra are AND ([[multiplication]]), OR ([[addition]]), and NOT. From these functions, the other functions of boolean algebra can be derived. | + | The three basic operations of boolean algebra are AND ([[multiplication]]), OR ([[addition]]), and NOT. See the table below for a numerical description. From these functions, the other functions of boolean algebra can be derived. |
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| 1 || 1 || 1 || 1 || 0 || 1 | | 1 || 1 || 1 || 1 || 0 || 1 | ||
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| − | AND | + | ===AND=== |
| + | AND is the boolean equivalent of multiplication. In words, the AND function states: "If A AND B are true then C is true". Numerically, the product of two numbers can only be non-zero if both numbers are non-zero. The AND function is commutative, so it works no matter what order the values are in. For example, A • B = B • A, and A • (B • C) = (A • B) • C. | ||
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| + | Just as in traditional [[algebra]], [[exponent]]s can be represented as a series of multiplications in boolean algebra, but the results are different. A<sup>n</sup> can be represented as the value A multiplied n times, or A•A•A•A... = C. Boolean multiplication returns a "true" (or a 1) if all values are "true" (or 1), but in this case, all values are always the same. So if A = 0, C = 0, and if A = 1, C = 1. This means that A<sup>n</sup> simply reduces to A! | ||
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{{clear}} | {{clear}} | ||
===test=== | ===test=== | ||
Revision as of 04:49, December 11, 2007
Boolean algebra is a division of mathematics which deals with boolean variables, which are variables which can only have two values. Typically these values are 0 and 1, especially within the fields of electronics or computers, however boolean variables can be other values, such as "true" and "false". Boolean algebra was invented in the nineteenth century by an English mathematician named George Boole.
Three Basic Operations
The three basic operations of boolean algebra are AND (multiplication), OR (addition), and NOT. See the table below for a numerical description. From these functions, the other functions of boolean algebra can be derived.
| AND: A•B=C | OR: A+B=C | NOT (A'=B) | |||||||
|---|---|---|---|---|---|---|---|---|---|
| A | B | C | A | B | C | A | B | ||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ||
| 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | ||
| 1 | 0 | 0 | 1 | 0 | 1 | ||||
| 1 | 1 | 1 | 1 | 0 | 1 | ||||
AND
AND is the boolean equivalent of multiplication. In words, the AND function states: "If A AND B are true then C is true". Numerically, the product of two numbers can only be non-zero if both numbers are non-zero. The AND function is commutative, so it works no matter what order the values are in. For example, A • B = B • A, and A • (B • C) = (A • B) • C.
Just as in traditional algebra, exponents can be represented as a series of multiplications in boolean algebra, but the results are different. An can be represented as the value A multiplied n times, or A•A•A•A... = C. Boolean multiplication returns a "true" (or a 1) if all values are "true" (or 1), but in this case, all values are always the same. So if A = 0, C = 0, and if A = 1, C = 1. This means that An simply reduces to A!
test
Boolean algebra is a mathematical system which is particularly important for computers. It consists of three logical statements AND, OR, and NOT operators. Each of the three operators corresponds to an algebraic operation. AND corresponds to multiplication, OR corresponds to division, NOT does not really have an algebraic equivalent. It has corallary terms such as NAND (NOT AND), NOR (NOT OR), and OT.
| A | B | C |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| A | B | C |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| α | cell2
|
the original table again |