Structured algorithm to extend the numeric range of n-bit binary number
Mainly, digital computer devices and digital signal processing technologies are dealing with binary number, a base-2 numbering system that consists of two states, zero and one. Computers store data and information using electronic switches in a cell of memory. The maximum capacity of data and information depends on the maximum number of bit that could be placed in the memory cell. Value types are the fundamental data types of programming language and the common types needed by most applications. In hierarchy, value types are further subdivided into structured types that are consisting of numeric types. A common numeric type that is used in programming is Integral data type or Integer. All integral values represent whole numbers, values without decimal notation or fraction, and ranging from negative to positive figures. The capacity of storage allocated to int values is either 32-bit or 64-bit, depending on the implementation of Objective-C on the platform or the CPU on which the compiler is running. For a 32-bit implementation, the maximum range of unsigned int values are 0 to 4294967295, and the maximum range of signed int values are -2,147,483,648 to +2,147,483,647. This paper conducts theoretical and practical research to attempt an advanced data processing. The author analyses and learns the data representations of computer hardware, then derives a fundamental concept for building a structured algorithm to enlarge the numeric range of n-bit binary number. The concept of the algorithm is built structurally, proved mathematically, and demonstrated briefly using 16-bit microcontroller simulation software and visual C# programming. The outcome of this research paper is expected to bring benefits in digital area of technology and meet the requirements of related computer applications.
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