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# We saw earlier that integer addition both unsigned

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Unformatted text preview: over the ½ values ¼ , giving numbers Î in the range ¼ to ¢ . ½¾ , and the fractions also range ½ ½·¼ ½ to ½ · , giving The smallest normalized numbers in this format also have ½ ½ over the values ¼ . However, the signiﬁcands then range from numbers Î in the range ½¾ to ½½¾ . Observe the smooth transition between the largest denormalized number ½¾ and the smallest normalized number ½¾ . This smoothness is due to our deﬁnition of for denormalized values. By making it ½ × rather than × , we compensate for the fact that the signiﬁcand of a denormalized number does not have an implied leading 1. As we increase the exponent, we get successively larger normalized values, passing through 1.0 and then to the largest normalized number. This number has exponent , giving a weight ¾ ½¾ . The fraction ½ equals giving a signiﬁcand Å . Thus the numeric value is Î ¾ ¼. Going beyond this overﬂows to ·½. 72 CHAPTER 2. REPRESENTING AND MANIPULATING INFORMATIO...
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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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