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# As we saw earlier none of these monotonicity

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Unformatted text preview: 0 01 10 11 Å Î ¾ ½ ¼ — — — — — — — — — — — — — — — — · ÆÆ ÆÆ ÆÆ ½ Figure 2.24 shows the representations and numeric values of some important single and double-precision ﬂoating-point numbers. As with the eight-bit format shown in Figure 2.23 we can see some general properties for a ﬂoating-point representation with a -bit exponent and an Ò-bit fraction: 74 Description Zero Smallest denorm. Largest denorm. Smallest norm. One Largest norm. exp ¼¼ ¼¼ ¼¼ ¼¼ ¼½ ½½ CHAPTER 2. REPRESENTING AND MANIPULATING INFORMATION frac ¼ ¼ ½ ¼ ¼ ½ ¡¡¡ ¡¡¡ ¡¡¡ ¡¡¡ ¡¡¡ ¡¡¡ ¼¼ ¼¼ ¼¼ ¼½ ½½ ½¼ ¡¡¡ ¡¡¡ ¡¡¡ ¡¡¡ ¡¡¡ ¡¡¡ Single Precision Value Decimal Double Precision Value Decimal ¾ ´½ ¼¼ ¼½ ½½ ¼¼ ¼¼ ½½ ¾¿ ¢ ¾ ½¾ ½¾ ´½ ¯µ ¢ ¾ ½¾ ½¢¾ ¾ ´¾ ¼ ½ ½¾ ½¾ ¢ ¯ ¢ ½ ¾ µ ¼ ¢ ¢ ¢ ¼¼ ½¼ ¿ ½¼ ¿ ½¼ ½¼ ¾ ½¾ ¿ ¢ ½¼ ¿ ´¾ ¢ ¯ ¢ ¢ ¢ ¯ ¢ ¾ ¾ µ ¾ ½ ¾ ½ ¾ ¼ ½¼¾¾ ½¼¾¾ ¾¾ ¾¾ ½¼¾¾ ¼ ¢ ¢ ¢ ¼¼ ¿¾ ¿¼ ½¼ ¿¼ ½¼ ½¼ ½¼ µ ¾ ½¼¾¿ ½ ¢ ½¼ ¿¼ Figure 2.24: Examples of Nonne...
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