14-Floating-Point-Arithmetic-4UP

14-Floating-Point-Arithmetic-4UP - IEEE-754 Arithmetic...

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Unformatted text preview: IEEE-754 Arithmetic Floating-Point Arithmetic Dhavide Aruliah UOIT MATH 2070U c D. Aruliah (UOIT) Floating-Point Arithmetic MATH 2070U 1 / 18 IEEE-754 Arithmetic Floating-Point Arithmetic 1 ANSI/IEEE 754-1985 2 Floating-point arithmetic c D. Aruliah (UOIT) Floating-Point Arithmetic MATH 2070U 2 / 18 IEEE-754 Arithmetic Binary floating-point number systems Floating point system = 2: F ( 2, t , e min , e max ) Bits = binary digits Binary machine numbers x F of the form x = (- 1 ) s m 2 e with m = ( 0.1 b 2 b 3 . . . b t | {z } = : M ) 2 = mantissa = significand Normalised binary numbers: leading bit always 1 Leading implicit bit need not be stored; store only M (last t- 1 digits) c D. Aruliah (UOIT) Floating-Point Arithmetic MATH 2070U 4 / 18 IEEE-754 Arithmetic IEEE floating-point single precision numbers Single precision: t = 24, e min =- 125, e max = 128 32 bits: 1 sign bit, 8 bit exponent, 23 bit mantissa s E (8 bits) M (23 bits) Exponent E biased: e = E- 126 (1 E 254) x min = smallest normalised number = 2- 126 ' 1.2 10- 38 x max = largest normalised number = 2 128 ( 1- 2- 24 ) ' 3.4 10 38 c D. Aruliah (UOIT) Floating-Point Arithmetic MATH 2070U 5 / 18 IEEE-754 Arithmetic IEEE floating-point double precision numbers Double precision: t = 53, e min =- 1021, e max = 1024 64 bits: 1 sign bit, 11 bit exponent, 52 bit mantissa s E (11 bits) M (52 bits) Exponent...
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This note was uploaded on 02/23/2010 for the course MATH 2070 taught by Professor Aruliahdhavidhe during the Spring '10 term at UOIT.

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14-Floating-Point-Arithmetic-4UP - IEEE-754 Arithmetic...

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