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A textbook of Computer Based Numerical and Statiscal Techniques part 5

A textbook of Computer Based Numerical and Statiscal Techniques part 5. By joining statistical analysis with computer-based numerical methods, this book bridges the gap between theory and practice with software-based examples, flow charts, and applications. Designed for engineering students as well as practicing engineers and scientists, the book has numerous examples with in-text solutions. | 26 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES The basic operations specified by IEEE arithmetic are first and foremost addition subtraction multiplication and division. Square roots and remainders are also included. The default rounding for these operationsis to nearest even . This means that the floating point result fl a op b of the exact operation a op b is the nearest floating point number to a op b breaking ties by rounding to the floating point number whose bottom bit is zero the even one . It is also possible to round up round down or truncate round towards zero . Rounding up and down are useful interval arithmetic which can provide guaranteed error bounds unfortunately most languages and or compilers provide no access to the status flag which can select the rounding direction. When the result of floating point operation is not representable as a normalized floating point number and exception occurs. 1.8 FLOATING POINT ARITHMETIC AND THEIR COMPUTATION The computer performed five basic arithmetic operations such as addition subtraction multiplication and division. The decimal numbers are converted to machine numbers. The machine number consists of only the digit 0 and 1 with a base. It s base depending on the computer. If the base is two the number system is called the binary number system if the base is eight it is called octal number system and if the base is sixteen it is called hexadecimal number system respectively. The decimal number system has the base 10. In numerical computation there are mainly two types of arithmetic operations present in the system. a Integer arithmetic which deals with integer operands and b Real or Floating-point arithmetic which deals with fractional part of a number as operands. Mostly computers carried out scientific calculations in floating point arithmetic to avoid the difficulty of keeping every number less than 1 in magnitude during computation. A floating point number is characterized by three parameters the .