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Unformatted text preview: erstanding ﬂoating-point numbers is to consider binary numbers having fractional values. Let us ﬁrst examine the more familiar decimal notation. Decimal notation uses a representation of the form: Ñ Ñ ½ ¡ ¡ ¡ ½ ¼ ½ ¾ ¡ ¡ ¡ Ò , where each decimal digit ranges between 0 and 9. This notation represents a number Ñ ½¼ Ò ¢ The weighting of the digits is deﬁned relative to the decimal point symbol ‘ ’: digits to the left are weighted by positive powers of ten, giving integral values, while digits to the right are weighted by negative powers of ten, giving fractional values. For example, ½¾ ¿ ½¼ represents the number ½ ¢ ½¼½ · ¾ ¢ ½¼¼ · ¿ ¢ ½¼ ½ · ¿ ¢ ½¼ ¾ ½¾ ½¼¼ . By analogy, consider a notation of the form Ñ Ñ ½ ¡ ¡ ¡ ½ ¼ ½ ranges between 0 and 1. This notation represents a number Ñ ¾ ¡ ¡ ¡ , where each binary digit, or bit, Ò ¾ ¢ (2.19) Ò The symbol ‘ ’ now becomes a binary point, with bits on the left being weighted by positive powers of t...
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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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