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Why is Boolean algebra important to digital computers?

The term “Boolean” has excessive usage in the fields of mathematics as well as computer science. What does it mean? In the disciple of Algebra, it defines variables that have only two flat values. The first one is “true” and second is “false”. The same logic is applied when you are declaring a variable in any software program. If it is categorized as Boolean, it would have one of these two values.

Boolean Algebra Operations

Students who study this mathematics topic should be well aware of the operations that can be applied on variables. For instance, if you have two variables A and B, the “De-Morgan” method would have the following implications.

−(A+B) =(−A−B)

It is not possible to parse this expression manually and good Boolean Algebra calculator needs to be used for effective results. This tool produces desired output for various expressions that involve two variables with true or false values. Apart from the De-Morgan principal, the same logic can be applied to solve XOR, Modus Ponens and other operations as well.

Significance of Boolean Algebra with respect to Digital Computing

It is a fact that the basic logic of this field of algebra is applied in digital computing. Let us go through the following points to see how this statement is factual.

  • There is a basic principle on the basis of which all digital computing concepts are based. According to it, the system memory stores data in the form of zeroes (“0”) and ones (“1”) only. The reason being that it understands this language only. Suppose that the word “character” has to be saved in the memory. It would not be stored in the original form. This is because, English language would not be recognized.
  • Every character stored in the memory is converted to zeroes and ones which is also termed as the binary form. A lot of people have questions about how information is retrieved according to digital computing standards. Let us reconsider the example of the word “character”. In case of retrieval, the binary code stored will be converted to the actual text again. After that, the user would be able to view it.
  • If you have a look at the conceptual definition of Boolean Algebra explained above, it shows that a variable can either be true or false. It cannot hold a third value or range of values. Similarly, in case of digital computing, everything is stored in the form of zeroes or ones.  Therefore, if you perform a logical comparison between the two, the same conceptual implication has been put into practice. Boolean variables have values of true and false which are equivalent to 0 and 1.

Role of Boolean Algebra in Digital Computing applications

There is no doubt that digital computing has countless uses. In addition to that, the role of variables with Boolean values is quite integral for most of them.

Computing Circuits

The word of software technology has advanced way beyond our imaginations but the value of quality hardware can never be ignored as a result. Digital computing is used in various computing circuits for motherboards, hard drive storage and other components. When information travels through them, it is in the form of a synapse wave. At one point, the value is 0 while at the other, it is 1.

  • Students who have previous knowledge of Boolean Algebra do not face problems in understanding the usage of digital computing. This is because the basics do not change. If you know how mathematical variables hold the values of “true” and “false”, it would be easy to understand how zeroes and ones are stored.

Memory storage and retrieval

A major implication of digital computing is related to how information is stored into the system memory and then retrieved from it. For better elaboration, we can consider the example of document with some information written on it.

  • The memory storage process will be executed when you save the document for the first time. Each word written will be converted to the corresponding binary value (0 and 1). After that, a memory location is defined for each binary value. It travels through data buses and then gets saved in the selected slot. It can be said that every bit saved in the memory would be either a zero or a one. In other words, it would be either true or false.
  • When you talk about the retrieval process, it is opposite of the one mentioned above. Suppose that you wish to open the saved document. The binary values of the written text would be retrieved and converted to high level language which can be interpreted by the human mind. We cannot understand the combinations of zeroes and ones. Once all the binary values have been extracted, we are able to see the text written on the document.

 

Summing it Up

Boolean Algebra is a sector of the mathematics field. It is based on the definition that a variable can hold the true or false value only. When you talk about digital computing, the logic does not alter a lot. Instead, data is stored in the form of 0 and 1. It is reconverted to the actual form when the user retrieves the related file.

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