Observe the smooth transition between the largest

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Unformatted text preview: wo, and those on the right being weighted by negative powers of two. For example, ½¼½ ½½¾ represents the ½ ½ ¿ number ½ ¢ ¾¾ · ¼ ¢ ¾½ · ½ ¢ ¾¼ · ½ ¢ ¾ ½ · ½ ¢ ¾ ¾ ·¼·½· · , ¾ One can readily see from Equation 2.19 that shifting the binary point one position to the left has the effect of dividing the number by two. For example, while ½¼½ ½½¾ represents the number ¿ , ½¼ ½½½¾ represents the ½ number ¾ · ¼ · ¾ · ½ · ½ ¾ . Similarly, shifting the binary point one position to the right has the effect ½ of multiplying the number by two. For example, ½¼½½ ½¾ represents the number · ¼ · ¾ · ½ · ¾ ½½ ½ . ¾ Note that numbers of the form ¼ ½½ ¡ ¡ ¡ ½¾ represent numbers just below ½. For example, sents ¿ . We will use the shorthand notation ½ ¼ ¯ to represent such values. ¼ ½½½½½½¾ repre- Assuming we consider only finite-length encodings, decimal notation cannot represent numbers such as ½ ¿ and exactly. Similarly, fractional binary notation can only r...
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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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