Select basic ads. Create a personalised ads profile. Select personalised ads. Apply market research to generate audience insights. Measure content performance. Develop and improve products. List of Partners vendors. Boolean algebra is a division of mathematics that deals with operations on logical values and incorporates binary variables. Boolean algebra traces its origins to an book by mathematician George Boole. The distinguishing factor of Boolean algebra is that it deals only with the study of binary variables.
Most commonly Boolean variables are presented with the possible values of 1 "true" or 0 "false". Variables can also have more complex interpretations, such as in set theory. Boolean algebra is also known as binary algebra. Boolean algebra is different from elementary algebra as the latter deals with numerical operations and the former deals with logical operations.
Elementary algebra is expressed using basic mathematical functions, such as addition, subtraction, multiplication, and division, whereas Boolean algebra deals with conjunction, disjunction, and negation. Since its concept has been detailed, Boolean algebra's primary use has been in computer programming languages.
Its mathematical purposes are used in set theory and statistics. Boolean algebra has applications in finance through mathematical modeling of market activities. For example, research into the pricing of stock options can be aided by the use of a binary tree to represent the range of possible outcomes in the underlying security.
In this binomial options pricing model , where there are only two possible outcomes, the Boolean variable represents an increase or a decrease in the price of the security. This type of modeling is necessary because, in American options, which can be exercised at any time, the path of a security's price is just as important as its final price.
The binomial options pricing model requires the path of a security's price to be broken into a series of discrete time ranges. As such, the binomial options pricing model allows an investor or trader to view the change in the asset price from one period to the next.
This law states that the order in which the logic operations are performed is irrelevant as their effect is the same. This law uses the NOT operation. The inversion law states that double inversion of a variable results in the original variable itself. Boolean Algebra Advertisements. Previous Page. Next Page. Logic has always straddled the line between philosophy and mathematics, attempting to reason about the way we can reason, and getting at fundamental ideas about what truth is and how to be sure we know things.
While fascinating, propositional logic and Boolean algebra initially belonged strictly to the realm of pure mathematics, with fewer applications than a branch of math like differential equations and calculus, which are at the foundation of our understanding of physics. Remarkably, about a century after Boole's initial investigations, mathematicians and scientists discovered an extremely powerful set of applications for formal logic, and now this apparently abstract mathematical and logical tool is at the heart of the global economy.
Wikimedia Commons Boolean algebra — taking true and false values, manipulating them according to logical rules, and coming up with appropriate true and false results — is the fundamental basis of the modern digital computer. One of the first major applications of Boolean algebra came from the master's thesis of Claude Shannon , one of the most important mathematicians and engineers of the 20th century. Shannon realized that switches in relay networks, like in a telephone network, or an early proto-computer, could be easily described by viewing "on" switches has having a Boolean value of "true", "off" switches as having a Boolean value of "false", and with the different patterns in which switches are connected to each other corresponding to the Boolean operations of "and", "or", and "not".
Shannon's innovation made the design of switch networks vastly easier: rather than needing to actually play around with network connections themselves, the techniques developed by Boole and his successors provided a mathematical framework allowing for more efficient network layouts. The connection between electrical switches and boolean algebra goes in the other direction as well. A computer's CPU is largely built out of logic gates : physical manifestations of Boolean operators.
Logic gates take in one or more electrical Boolean values: a wire with a high voltage might represent "true", and a wire with a low voltage might represent "false". The output of the logic gate, calculated using the electronic properties of semiconductors, is the appropriate voltage from the desired Boolean operation.
An "and" gate, for example, takes in two inputs. If both inputs are high voltage representing "true" , the "and" gate has a high voltage output of "true" as well, while if either or both inputs are low voltage, or false, the gate will have a low voltage output of false. Putting these gates together in the right ways allows for the execution of computer programs.
Being able to perform Boolean operations on various inputs essentially allows a CPU to decide how to handle those inputs. Further, this Boolean algebra embedded in computers comes back around to normal math. The Boolean dichotomy of true vs.
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