4834_lecture_19_ho

4834_lecture_19_ho - EEL 4834 Lecture 19 EEL 4834 Lecture...

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Unformatted text preview: EEL 4834: Lecture 19 EEL 4834: Lecture 19 Floating Point Serialization Professor O. Boykin University of Florida, Department of Electrical and Computer Engineering October 13, 2009 EEL 4834: Lecture 19 Outline 1 IEEE 754 2 Serialization EEL 4834: Lecture 19 IEEE 754 IEEE 754 Standard Modern computers are binary with fixed size registers. We need to be able to represent real numbers in fixed length binary. IEEE 754 (standardized in 1985) is a standard for representing floating point numbers in binary, used by all common computers. EEL 4834: Lecture 19 IEEE 754 Type Exponent Fraction Normalized 1 to 2 e- 2 any Denormalized any ∞ 2 e- 1 NaNs 2 e- 1 non-zero EEL 4834: Lecture 19 IEEE 754 Single Precision IEEE 754 floating point number has value v = s × 2 e × m where: Normalized (Exponent 6 = 0): s (- 1) s b where s b is the sign bit e Exponent - 127 m 1.fraction in binary. Denormalized (Exponent = 0) s (- 1) s b e-126 (NOT -127) m 0.fraction in binary. The above gives us: 1 × 2 124- 127 × (1 + 0 × 2- 1 + 1 × 2- 2 ) = 1 . 25 × 2- 3 = 0 . 15625....
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This note was uploaded on 02/11/2010 for the course EEL 4834 taught by Professor Staff during the Fall '08 term at University of Florida.

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4834_lecture_19_ho - EEL 4834 Lecture 19 EEL 4834 Lecture...

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