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Unformatted text preview: the set of values that can be represented in a hypothetical 6-bit format having ¿ ¿ ½ exponent bits and Ò ¾ signiﬁcand bits. The bias is ¾ ½ ¿. Part A of the ﬁgure shows all representable values (other than Æ Æ ). The two inﬁnities are at the extreme ends. The normalized numbers with maximum magnitude are ¦½ . The denormalized numbers are clustered around 0. These can be seen more clearly in part B of the ﬁgure, where we show just the numbers between ½ ¼ and ·½ ¼. The two zeros are special cases of denormalized numbers. Observe that the representable numbers are not uniformly distributed—they are denser nearer the origin. Figure 2.23 shows some examples for a hypothetical eight-bit ﬂoating-point format having exponent ½ ½ bits and Ò ¿ fraction bits. The bias is ¾ . The ﬁgure is divided into three regions representing the three classes of numbers. Closest to 0 are the denormalized numbers, starting with 0 itself. Denormalized ½ numbers in this format have ½ , giving a weight ¾ . The fractions range...
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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.
- Spring '10
- The American