Semiconductor & Computer Engineering
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Today, Boolean algebra is the primary mathematical tool used in designing modern digital systems. Switching functions are described using Boolean algebra since they deal with two discrete states - ON and OFF (or 1 and 0). Those functions are in turn implemented via [[transistors]] which act as switches, a natural implementation for representing Boolean algebra operations. Once primitive Boolean operation circuits such as [[NOT]], [[AND]], and [[OR]] [[logic gates|gates]] are implemented, any conceivable system of logic can be implemented using them like Lego pieces. | Today, Boolean algebra is the primary mathematical tool used in designing modern digital systems. Switching functions are described using Boolean algebra since they deal with two discrete states - ON and OFF (or 1 and 0). Those functions are in turn implemented via [[transistors]] which act as switches, a natural implementation for representing Boolean algebra operations. Once primitive Boolean operation circuits such as [[NOT]], [[AND]], and [[OR]] [[logic gates|gates]] are implemented, any conceivable system of logic can be implemented using them like Lego pieces. | ||
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| + | == Variables == | ||
| + | Boolean algebra uses variables just like normal algebra. Those variables can only have one of two values - either a 0 or a 1. Variable are commonly represented as a single alphabet letter. While there is no one acceptable convention, a it's not uncommon to see letters such as <math>A, B, \text{ and } C</math> used for inputs and <math>P, Q, R, \text{ and } Z</math> for output. That's also the convention used on WikiChip. Sometimes it's desired to represent the [[negated]] (opposite) value of a variable, that's often done with a bar or a tick (prime) above or next to the letter, for example <math>\bar A</math> or <math>\neg B</math> although [[negation|other values are possible]]. | ||
Revision as of 17:39, 28 November 2015
Boolean algebra (or less commonly symbolic logic) is a branch algebra that deals with only two logic values - 0 (corresponding to false) and 1 (corresponding to true).
Today, Boolean algebra is the primary mathematical tool used in designing modern digital systems. Switching functions are described using Boolean algebra since they deal with two discrete states - ON and OFF (or 1 and 0). Those functions are in turn implemented via transistors which act as switches, a natural implementation for representing Boolean algebra operations. Once primitive Boolean operation circuits such as NOT, AND, and OR gates are implemented, any conceivable system of logic can be implemented using them like Lego pieces.
Variables
Boolean algebra uses variables just like normal algebra. Those variables can only have one of two values - either a 0 or a 1. Variable are commonly represented as a single alphabet letter. While there is no one acceptable convention, a it's not uncommon to see letters such as used for inputs and for output. That's also the convention used on WikiChip. Sometimes it's desired to represent the negated (opposite) value of a variable, that's often done with a bar or a tick (prime) above or next to the letter, for example or although other values are possible.