13-Floating-Point-Number-Systems-4UP

13-Floating-Point-Number-Systems-4UP - Floats Examples...

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Unformatted text preview: Floats Examples Properties Floating Point Number Systems Dhavide Aruliah UOIT MATH 2070U c D. Aruliah (UOIT) Floating Point Number Systems MATH 2070U 1 / 20 Floats Examples Properties Floating Point Number Systems 1 Floating-point number systems 2 Examples 3 Properties of floating point number systems c D. Aruliah (UOIT) Floating Point Number Systems MATH 2070U 2 / 20 Floats Examples Properties Machine numbers Machine numbers : numbers representable in a computer Conceptually represented in sequence of boxes Example: 6 digit base 10 fixed point number system: . 0 . 0 1 . 0 2 . . . 9 9 9 . 9 9 9 x min = 0.001 = 10- 3 x max = 999.999 ' 10 4 10 6 possible nonnegative machine numbers c D. Aruliah (UOIT) Floating Point Number Systems MATH 2070U 4 / 20 Floats Examples Properties Scientific notation Scientific notation superseded fixed point notation Permits wider range of values with fixed # of symbols Multiply through by powers of 10 to shift decimal to right or left- 1370.1542 =- 0.13701542 10 4 ' - 0.137015 10 04 0.0000009376 = 0.9376 10- 6 Terminology: if x = m 10 e = ( a 1 a 2 . . . a t ) 10 10 e I m = ( a 1 a 2 . . . a t ) 10 = mantissa I e = exponent I a 1 = most significant digit I a t = least significant digit c D. Aruliah (UOIT) Floating Point Number Systems MATH 2070U 5 / 20 Floats Examples Properties Normalised scientific notation Many representations of same number possible, e.g.,- 1370 =- 1370 10 =- 137.0 10 1 =- 13.70 10 2 =- 0.1370 10 4 =- 0.001370 10 6 =- 13700000 10- 4 Normalise : leading nonzero digit to left of decimal point, e.g.,- 1370 =- 0. 1 370 10 4 Distinct normalisations possible, e.g.,- 1.370 10 3 Same idea works in other bases, e.g., ( 1A5 . 9E ) 16 16 = ( . 1A59E ) 16 16 3 c D. Aruliah (UOIT) Floating Point Number Systems MATH 2070U 6 / 20 Floats Examples Properties Floating-point number systems Definition (Floating-point number system)...
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13-Floating-Point-Number-Systems-4UP - Floats Examples...

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