fp - CSE 341 Floating Point Operations Floating Point...

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CSE 341 Floating Point Operations Floating Point Numbers Scientific Notation Normalized numbers No leading zeros Binary 1. xxx 2 x 2 yy Fixed Point vs. Floating Point Advantages of Floating Point Normalized Form Simplified data exchange Simplified arithmetic Increased accuracy Floating Point Representation Accuracy vs. Range Number of bits for significand vs. number of bits for exponent Sign-magnitude Notation Single Precision Format Double Precision Single vs. Double Precision MIPS formats conform to IEEE 754 floating point standard Leading 1 is implicit Increases number of bits stored in significand by 1 Biased Exponents Single Precision -126 127 Bias: 127 S 1 Bits Exponent (E) (-1) X 1.F X 2 S (E-bias) 8 Significand (F) 23 S 1 Bits Exponent (E) (-1) X 1.F X 2 S (E-bias) 11 Significand (F) 52
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Double Precision -1022 1023 Bias: 1023 All 1’s in exponent indicate out of range 21.8125 10101.1101 2 Normalized 1.01011101 2 x 2 4 Exponent 127+4 = 131 = 10000011 Significand 01011101 Sign 0 Number 01000001101011101000000000000000 Accelerated sorting of floating point numbers Integer comparisons Keys Order of fields Use of biased exponents Overflow Exponent too large to be represented in exponent Underflow Exponent too small to be represented in exponent
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fp - CSE 341 Floating Point Operations Floating Point...

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