H chapter 2 representing and manipulating information

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Unformatted text preview: gative Floating-Point Numbers. ¯ ¯ ¯ ¯ ¯ ¯ The value ·¼ ¼ always has a bit representation of all ¼’s. The smallest positive denormalized value has a bit representation consisting of a 1 in the least signif Ò and an icant bit position and otherwise all 0s. It has a fraction (and significand) value Å ¾ ½ ·¾ exponent value ¾ ½ · ¾. The numeric value is therefore Î ¾ Ò ¾ . The largest denormalized value has a bit representation consisting of an exponent field of all 0s and Ò (which we a fraction field of all 1s. It has a fraction (and significand) value Å ½ ¾ have written ½ ¯) and an exponent value ¾ ½ · ¾. The numeric value is therefore Î Ò µ ¢ ¾ ¾ ½ ·¾ , which is just slightly smaller than the smallest normalized value. ´½ ¾ The smallest positive normalized value has a bit representation with a 1 in the least signicant bit of the exponent field and otherwise all 0s. It has a significand value Å ½ and an exponent value ¾ ½ · ¾. The...
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