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float - 7(normalized binary floating point IEEE Floating...

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Binary equivalent of a real number The integer and fraction parts are converted independently. Suitable methods are repeated division by 2 (integer part) and repeated multiplication by 2 (fraction part). After putting these two parts together to form a binary fixed point number, add a zero exponent to get the number into binary floating point form. Then normalize by moving the decimal point to obtain a number in the form 1.xxxxxxxx E ee . Example : Convert 200.6875 to normalized binary floating point form. Integer Part Fraction 200 .6875 100 R 0 1 .375 50 R 0 0 .75 25 R 0 1 .5 12 R 1 1. 0 6 R 0 3 R 0 1 R 1 0 R 1 200.6875 = 11001000.1011b x 2 0 = 1.10010001011b x 2
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Unformatted text preview: 7 (normalized binary floating point) IEEE Floating Point Representations Short Real (Doubleword, 32 bits) Long Real (Quadword, 64 bits) IEEE Short Real Format SXXX XXXX XFFF FFFF FFFF FFFF FFFF FFFF S : Sign bit 0. .positive 1. .negative X : 8-bit exponent in excess-127 form F : 23-bit fraction; leading 1 is not stored Example : Derive the IEEE Short Real format of 200.6875 200.6875 = 1.10010001011b x 2 7 (normalized) S : 0 (positive) X : 100 0011 0 (127 + 7) F : 100 1000 1011 0000 0000 0000 (integer 1 digit not stored) IEEE Short Real: 0100 0011 0100 1000 1011 0000 0000 0000 or 4348B000h...
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