tailieunhanh - Modeling of Combustion Systems A Practical Approach 6

Tham khảo tài liệu 'modeling of combustion systems a practical approach 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Appendix F Numbers in Binary Octal and Hexadecimal Representations For readers unfamiliar with binary and related bases we digress here to consider three important numerical systems besides the decimal base 10 system these are binary base 2 octal base 8 and hexadecimal base 16 . Obviously the decimal system uses ten number symbols 0 1 2 3 4 5 6 7 8 9 that multiply 10 raised to some exponent. The system is positional with columns to the left of the decimal point indicating increasing powers of 10 and those to the right decreasing powers. For example may be written as 2 102 3 101 4 100 5 10-1 200 30 4 5 10 . Table illustrates the procedure. TABLE Positional Number Representation in Base 10 . Exponent 3 2 1 0 . -1 -2 -3 . Exponential notation 103 102 101 100 . 10-1 10-2 10-3 . Decimal notation . 1000 100 10 1. 1 10 1 100 1 1000 . Decimal multipliers 2 3 4 . 5 Decimal sum 200 30 4 . 5 10 By analogy octal base 8 uses an analogous scheme eight number symbols 0 1 2 3 4 5 6 7 and a base of 8. To see what the octal equivalent of is we refer to Table and find that . The subscript after the number indicates the base. Obviously if there is no subscript we are referring to base 10. TABLE Positional Number Representation in Base 8 . Exponent . 3 2 1 0. -1 -2 -3 . Exponential notation . 83 82 81 80 . 8-1 8-2 8-3 . Decimal notation . 512 64 8 1. 1 8 1 64 1 512 . Octal multipliers 3 5 2. 4 Decimal sum 192 40 2. 4 8 609 2006 by Taylor Francis Group LLC 610 Modeling of Combustion Systems A Practical Approach Base 2 is ideal for constructing factorial designs because the system comprises only two states for any factor high and low. In base 2 the only numbers we may use are 0 or 1. We can use - and in lieu of numeric symbols but the point is that we only have two symbols at our disposal. As an example of binary math the decimal number is equivalent to . Table shows why. TABLE .

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