09f_cpe431_chap3_3 - Single Precision Double Precision 2...

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1 1 Electrical and Computer Engineering CPE 431/531 Chapter 3 - Arithmetic for Computers Dr. Rhonda Kay Gaede UAH Electrical and Computer Engineering Page 2 of 5 UAH CPE 431/531 Chapter 3 (4 th Ed.) 3.1 Introduction Bits are bits, what is important is how they are interpreted. You may have an instruction. You may have a signed number (integer). You may have an unsigned number (integer). You may have a floating-point number. Electrical and Computer Engineering Page 3 of 5 UAH CPE 431/531 Chapter 3 (4 th Ed.) 3.5 Floating Point - Basics • Floating-point numbers are represented in scientific notation. _________________________ • Floating-point numbers use ________________ representation. • In general, floating-point numbers are of the form • IEEE defines two types of floating-point numbers
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Unformatted text preview: Single Precision Double Precision 2 Electrical and Computer Engineering Page 4 of 5 UAH CPE 431/531 Chapter 3 (4 th Ed.) 3.6 Floating Point More of the Story IEEE 754 Floating Point Standard Adding a bias to the exponent simplifies sorting The leading one is implicit Representation expanded Example: Represent -0.75 in single and double precision Electrical and Computer Engineering Page 5 of 5 UAH CPE 431/531 Chapter 3 (4 th Ed.) 3.7 Parallelism and Computer Arithmetic: Associativity Because floating-point numbers are approximations of real numbers and because computer arithmetic has limited precision, associativity does not hold for floating-point numbers. x = -1.5 10 x 10 38 , y = 1.5 10 x 10 38 , z = 1.0...
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09f_cpe431_chap3_3 - Single Precision Double Precision 2...

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