CP15_eps - 1 1 Machine precision and errors 2 Machine...

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Unformatted text preview: 1 1 Machine precision and errors 2 Machine representation and precision Every computer has a limit how small or large a number can be A computer represent numbers in the binary form. Word length: number of bytes used to store a number Most common architecture: Word length = 4 bytes = 32 bites Word length = 8 bytes = 64 bites ( 1 byte = 1 B = 8 bits: 00000000 ) 3 Integer numbers For a 8 bit computer The highest number then: 2 8 1 (1 because the first is 0) Since we need 1 bit for +/- Then the highest number is 2 7 1 = 127 For 32-bit computers all integer numbers are in the range 2 31 1 = 2,147,483,647 1 2 3 4 5 6 7 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 4 Floating point numbers------------------------ Three blocks ----------------------------- 0 1000 0000 1000000 0000 0000 0000 0000 signbit 8-bit exponent 23-bit mantissa range of exponent [-127,128] Single precision : 6-7 decimal places Double precision : 15-16 decimal places 127 exp 2 ) 1 ( = mantissa x S float 7 23 10 2 . 1 2 1 15...
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CP15_eps - 1 1 Machine precision and errors 2 Machine...

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