Round to even also called round to nearest is the

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Unformatted text preview: recision and ½¼¾¾ to ·½¼¾¿ for double precision. The fraction field frac is interpreted as representing the fractional value , where ¼ ½, having binary representation ¼ Ò ½ ¡ ¡ ¡ ½ ¼ , that is, with the binary point to the left of the most significant bit. The significand is defined to be Å ½ · . This is sometimes called an implied leading 1 representation, because we can view Å to be the number with binary representation ½ Ò ½ Ò ¾ ¡ ¡ ¡ ¼ . This representation is a trick for getting an additional bit of precision for free, since we can always adjust the exponent so that significand Å is in the range ½ Å ¾ (assuming there is no overflow). We therefore do not need to explicitly represent the leading bit, since it always equals 1. Denormalized Values When the exponent field is all 0s, the represented number is in denormalized form. In this case, the exponent value is ½ × , and the significand value is Å , that is, the value of the fraction field without an implied leading 1. Aside: Why...
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This note was uploaded on 09/02/2010 for the course ELECTRICAL 360 taught by Professor Schultz during the Spring '10 term at BYU.

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