FLOATING POINT FORMATS
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1 APPENDIX O FLOATING POINT FORMATS Paragraph Title Page 1.0 Introduction... O IEEE Bit Single Precision Floating Point... O IEEE Bit Double Precision Floating Point... O MIL STD 1750A 32 Bit Single Precision Floating Point... O MIL STD 1750A 48 Bit Double Precision Floating Point... O DEC 32 Bit Single Precision Floating Point... O DEC 64 Bit Double Precision Floating Point... O DEC 64 Bit G Double Precision Floating Point... O IBM 32 Bit Single Precision Floating Point... O IBM 64 Bit Double Precision Floating Point... O TI (Texas Instruments) 32 Bit Single Precision Floating Point... O TI (Texas Instruments) 40 Bit Extended Precision Floating Point... O-5 LIST OF TABLES Table O-1. Floating Point Formats... O-1 CHANGES TO THIS EDITION OF APPENDIX O Updates to this Appendix are in blue font. The blue font indicates either a completely new item or an update to a previously existing item. Paragraph 8.0 is entirely new.
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3 1.0 Introduction APPENDIX O FLOATING POINT FORMATS Table O-1 provides a summary of floating point formats. Details of each format are shown on the pages following the table. TABLE O-1. FLOATING POINT FORMATS Type Size Radix Sign Exponent Fraction Bias Formula IEEE_ (-1 S )(1.F)(2 (E-127) ) IEEE_ (-1 S )(1.F)(2 (E-1023) ) 1750A_ (0.F)(2 E ) 1750A_ (0.F)(2 E ) DEC_ (-1 S )(0.1F)(2 (E-128) ) DEC_ (-1 S )(0.1F)(2 (E-128) ) DEC_64G (-1 S )(0.1F)(2 (E-1024) ) IBM_ (-1 S )(0.F)(16 (E-64) ) IBM_ (-1 S )(0.F)(16 (E-64) ) TI_ ((-2) S + (0.F))(2 E ) TI_ ((-2) S + (0.F))(2 E ) O-1
4 2.0 IEEE Bit Single Precision Floating Point Value = (-1 S )(1.F)(2 (E-127) ) Exponent = power of 2 with bias of 127 Fraction = F portion of 23 bit fraction 1.F 0: E = 0, F = IEEE Bit Double Precision Floating Point Value = (-1 S )(1.F)(2 (E-1023) ) Exponent = power of 2 with bias of 1023 Fraction = F portion of 52 bit fraction 1.F 0: E = 0, F = MIL STD 1750A 32 Bit Single Precision Floating Point S Fraction Exponent Value = (0.F)(2 E ) S + Fraction = Normalized, 2's complement F portion of 24 bit fraction 0.F (Bit 2 MUST be set for positive, clear for negative) O-2
5 5.0 MIL STD 1750A 48 Bit Double Precision Floating Point S Fraction (MSW) Exponent Fraction Value = (0.F)(2 E ) S + Fraction = Normalized, 2's complement F portion of 40 bit fraction 0.F (Bit 2 MUST be set for positive, clear for negative) 6.0 DEC 32 Bit Single Precision Floating Point Value = (-1 S )(0.1F)(2 (E-128) ) Exponent = power of 2 with bias of 128 Fraction = F portion of 23 bit fraction 0.1F 0: S = 0 & F = 0 & E = DEC 64 Bit Double Precision Floating Point Value = (-1 S )(0.1F)(2 (E-128) ) Exponent = power of 2 with bias of 128 Fraction = F portion of 55 bit fraction 0.1F 0: S = 0 & F = 0 & E = 0 O-3
6 8.0 DEC 64 Bit G Double Precision Floating Point Value = (-1 S )(0.1F)(2 (E-1024) ) Exponent = power of 2 with bias of 1024 Fraction = F portion of 52 bit fraction 0.1F 0: S = 0 & F = 0 & E = IBM 32 Bit Single Precision Floating Point Value = (-1 S )(0.F)(16 (E-64) ) Exponent = power of 16 with bias of 64 Fraction = Normalized F portion of 24 bit fraction 0.F (Bits 9-12 cannot be all zero) 10.0 IBM 64 Bit Double Precision Floating Point Value = (-1 S )(0.F)(16 (E-64) ) Exponent = power of 16 with bias of 64 Fraction = Normalized F portion of 56 bit fraction 0.F (Bits 9-12 cannot be all zero) O-4
7 11.0 TI (Texas Instruments) 32 Bit Single Precision Floating Point Exponent S Fraction Value = ((-2) S +(0.F))(2 E ) Fraction = 2's complement F portion of 24 bit fraction 1.F 0: E = TI (Texas Instruments) 40 Bit Extended Precision Floating Point Exponent S Fraction Value = ((-2) S +(0.F))(2 E ) Fraction = 2's complement F portion of 32 bit fraction 1.F 0: E = -128 **** END OF APPENDIX O **** O-5
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