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Karnaugh Maps and Grey Code

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Boolean algebra was found to be a laborious and awkward way of simplifying expressions. However, these challenges were dealt with by the introduction of the Karnaugh maps. In reference to Lipschutz (1982), Karnaugh maps are pictorial devices for finding prime implicants and minimal-sum for Boolean expressions involving at most six variables (p.195). In other words, Karnaugh maps or rather K-maps are a means of minimizing the Boolean logic expressions by looping together groups of logic values. Notably, the size of the Karnaugh maps relies on the number of combinational logic circuit inputs. The Karnaugh map was first introduced by Edward W. Veitch in 1952 and further developed by Maurice Karnaugh in 1953.

On the other hand, the Grey Code is a numbering system that is commonly found in digital audio systems. In reference to Borwick & Association of Professional Recording Services (1996), the grey code is a code in which the counting system is arranged so that at each count, only one of the bit position changes state (p.50). In other words, two successive values in this code system are differentiated by only one value. The Grey Code is in some way related to the Karnaugh map.

Following this point, it is important to note that the Grey Code is utilized in most cases by the Karnaugh map to locate adjacent links. According to Crowe & Hayes-Gill (1998), the Karnaugh maps are based on the same principle as the Grey Code in the sense that the adjacent variables in the Karnaugh map are only differentiated by a single variable (p.67). In other words, both the Grey Code and the Karnaugh maps use the same principle in numbering their codes. With this in mind, it can be argued that Karnaugh maps and the Grey Code play a critical role in simplifying Boolean algebra expressions.

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