Computer Number Representation Scientific/Engineering Notation The speed of light c=+029792458×10t9ms in engineering sign mantissa exponents notation or0.299795498E09m/s o number of bits stored for exponents->the range of the number o number of bits stored for mantissa the number of significant bits o Search for a compromise. 1口“4元，4元↑重QC Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/20159/103
Computer Number Representation Scientific/Engineering Notation The speed of light c = + |{z} 0.299792458 | {z } ×10 +9 |{z}m/s sign mantissa exponents or 0.299795498 E09 m/s in engineering notation number of bits stored for exponents → the range of the number number of bits stored for mantissa → the number of significant bits Search for a compromise. Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/2015 9 / 103
Computer Number Representation Scientific/Engineering Notation The speed of light +9 c=、+0.299792458×10m/s in engineering sign mantissa exponents notation or0.299795498E09m/s o number of bits stored for exponents->the range of the number o number of bits stored for mantissa the number of significant bits o Search for a compromise. 1口“4元，4元↑重QC Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/20159/103
Computer Number Representation Scientific/Engineering Notation The speed of light c = + |{z} 0.299792458 | {z } ×10 +9 |{z}m/s sign mantissa exponents or 0.299795498 E09 m/s in engineering notation number of bits stored for exponents → the range of the number number of bits stored for mantissa → the number of significant bits Search for a compromise. Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/2015 9 / 103
Computer Number Representation Scientific/Engineering Notation The speed of light +9 c-、+0.299792458×10m/s in engineering sign mantissa exponents notation or0.299795498E09m/s o number of bits stored for exponents->the range of the number o number of bits stored for mantissa the number of significant bits o Search for a compromise. 1口“4元，4元↑重QC Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/20159/103
Computer Number Representation Scientific/Engineering Notation The speed of light c = + |{z} 0.299792458 | {z } ×10 +9 |{z}m/s sign mantissa exponents or 0.299795498 E09 m/s in engineering notation number of bits stored for exponents → the range of the number number of bits stored for mantissa → the number of significant bits Search for a compromise. Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/2015 9 / 103
Computer Number Representation Floating-point Notation ■■■■… sign exponent mantissa Sign (s) Exponent (e Fraction (f Bias Single Precision 131 830-23 2322-00 127 Double Presicion 1 163 11「62-521 52[51-00 1023 Table:IEEE 754 standard for floating-point arithmetic. 至0QC Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/2015 10/103
Computer Number Representation Floating-point Notation Sign (s) Exponent (e) Fraction (f) Bias Single Precision 1 [31] 8 [30-23] 23 [22-00] 127 Double Presicion 1 [63] 11 [62-52] 52 [51-00] 1023 Table: IEEE 754 standard for floating-point arithmetic. Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/2015 10 / 103
Computer Number Representation Floating-point Notation sign exponent mantissa Sign(s)Exponent(e) Fraction(f) Bias Single Precision 1 [31] 8[30-23] 23[22-00] 127 Double Presicion 1 [63] 11[62-52] 52[51-00] 1023 Table:IEEE 754 standard for floating-point arithmetic. 重090 Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/2015 10/103
Computer Number Representation Floating-point Notation Sign (s) Exponent (e) Fraction (f) Bias Single Precision 1 [31] 8 [30-23] 23 [22-00] 127 Double Presicion 1 [63] 11 [62-52] 52 [51-00] 1023 Table: IEEE 754 standard for floating-point arithmetic. Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/2015 10 / 103