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Unformatted text preview: tations to derive a numerical relationship. Comparing Equations 2.1 and 2.2, we can see that for bit pattern Ü, if we compute the difference ¾Í Û ´Üµ ¾Ì Û ´Üµ, the weighted sums for bits from 0 to Û ¾ will cancel each other, leaving a value: ¾Í Û ´Üµ ¾Ì Û ´Üµ ÜÛ ½ ´¾Û ½ ¾Û ½ µ ÜÛ ½ ¾Û . This gives a relationship ¾Í Û ´Üµ ÜÛ ½ ¾Û · ¾Ì Û ´Üµ. If we let Ü ¾Ì Û ´Üµ, we then have ¾Í Û ´Ì¾ Û´ Üµµ Ì¾Í Û ´Üµ Ü ½ ¾
Û Û · Ü (2.3) This relationship is useful for proving relationships between unsigned and two’s complement arithmetic. In the two’s complement representation of Ü, bit ÜÛ ½ determines whether or not Ü is negative, giving Ì¾Í Û ´Üµ ´ Ü·¾ Ü Û Ü Ü ¼ ¼ (2.4) Figure 2.11 illustrates the behavior of function Ì¾Í . As it illustrates, when mapping a signed number to its unsigned counterpart, negative numbers are converted to large positive numbers, while nonnegative numbers remain unchanged. Practice Problem 2.14:
Explain how Equation 2.4 applies to the entries in the table you generated when solving Problem 2.13. Going in th...
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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