International Journal of Computer Applications (0975 – 8887) Volume 160 – No 3, February 2017 45 Simplified Theorem in Number System Conversion Jennifer Bagulaya-Abogaa College of Computer Studies, Eastern Samar State University Borongan City, Eastern Samar, Philippines ABSTRACT Numbers found on computer were represented in 0s and 1s or bits, from binary digits. These numbers are identified from their bases. They can be converted from one number to another number. The researcher innovate simplified theorem in conversion of these numbers in simple mathematical operation. Conversion of these numbers were presented in conventional and exhausted manner in most references, it involves two or more variety of operation. This innovative tool is very easy to learn and very efficient. Three attributes; usability, reliability, and efficiency were employed to ascertain the applicability of the simplified theorem as tool for instruction. General Terms Conversion, Conventional, Decimal, Simplified Keywords Binary, Base, Efficiency, Hexadecimal, Octal, Innovative Tool, Number System, Reliability, Simplified Theorem, Usability. 1. INTRODUCTION Education is a light that shows the mankind the right direction to surge. The purpose of education is not just making student literate but adds rationale thinking, knowledge ability, and self sufficiency. When there is a willingness to change, there is hope for progress in any field. Creativity can be developed and innovation benefits both students and teachers (Damodharanan, 2013). There are many innovative and interesting proof techniques in the history of mathematics. One that comes to mind is the technique of diagonalization introduced by Cantor in his work on cardinalities of sets. Diagonalization is powerful, as it lets us prove non-existence results. Diagonalization has been used e.g. in the theory of computational complexity to show “gap theorems”. It is also the key to proving Godel’s famous incompleteness theorem, (Hyttel, 2013). Another theory developed in the discipline of mathematics is the multiple intelligence by Gardner. Howard Gardner (1991, p 12) argues in favor of approaching a discipline in a variety of ways that accommodate multiple learning styles, thereby facilitating the learning process more effectively, “The broad spectrum of students-and perhaps the society as a whole- would be better served if disciplines could be presented in a numbers of ways and learning could be assessed through a variety of means.” One strategy involves approaching multiplication facts in different way. Instead of having students commit all the multiplication facts to memory through repetition, the teacher could write one multiplication fact on the board (e.g. 6 x 4 = 24). Then the students could begin working with this fact in a variety of ways. The logical/mathematical learners would be able to write down all eight facts in the family, focusing on the logical relations of the facts. The verbal-linguistic learners would be able to write the multiplication fact using only words. They would also be able a word problem that requires the multiplication fact given in order to solve the word problem. The Visual-spatial learners would be able to draw a picture to represent the multiplication fact (Gardner, 1991). Number system consist of four numbers; binary numbers, decimal numbers, octal numbers, and hexadecimal numbers. Numbers were clearly presented in Discrete Structures and Discrete Mathematics computing courses. Khan (2013) narrated, “digital computer represents all kinds of data and information in the binary system. Binary Number System consists of two digits 0 and 1. Its base is 2. Each digit or bit in binary number system can be 0 or 1. A combination of binary numbers may be used to represent different quantities like 100. The Decimal Number System consists of ten digits from 0 to 9. These digits can be used to represent any numeric value. The base of decimal number system is 10. It is the most widely used number system. Octal Number System consists of eight digits from 0 to 7. The base of octal system is 8. Each digit position in this system represents a power of 8. Any digit in this system is always less than 8. Octal number system is used as a shorthand representation of long binary numbers. The Hexadecimal Number System consists of 16 digits from 0 to 9 and A to F. The alphabets A to F represent decimal numbers from 10 to 15. The base of this number system is 16. Each digit position in hexadecimal system represents a power of 16.” These number can be converted from one number to another. Conversion of these numbers are presented in conventional and exhausted manner in most references, it involves two or more variety of operations. The researcher innovate simplified theorem in conversion for these numbers in single mathematical operation. Hence, conformed this study. 2. OBJECTIVES The study aimed to (1) come-up a simplified theorem in number system conversion; and (2) evaluate the innovative tool using the attributes of reliability, usability, and efficiency. 3. SIMPLIFIED THEOREM General Instruction: Give attention the 1s or 1 bit. Simplified theorem. Express the decimal value per binary number, add those with 1s. 1 1 1 1 …8 4 2 1