Figure 213 shows some sample relational expressions

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Unformatted text preview: e other direction, we wish to derive the relationship between an unsigned number Ü and its signed counterpart Í¾Ì Û ´Üµ. If we let Ü ¾Í Û ´Üµ, we have ¾Ì Û ´Í¾ Û´ ܵµ Í¾Ì Û ´Üµ Ü Û ½ ¾ Û · Ü (2.5) 2.2. INTEGER REPRESENTATIONS 2w 2w–1 Unsigned 47 +2w–1 0 Two’s Complement 0 –2w–1 Figure 2.12: Conversion From Unsigned to Two’s Complement. greater than ¾Û ½ ½ to negative values. Function Í¾Ì converts numbers In the unsigned representation of Ü, bit ÜÛ ½ determines whether or not Ü is greater than or equal to ¾Û ½ , giving Í¾Ì Û ´Üµ ´ Ü Ü ¾ Û Ü Ü ¾ ¾ Û Û ½ ½ (2.6) This behavior is illustrated in Figure 2.12. For small ( ¾Û ½ ) numbers, the conversion from unsigned to signed preserves the numeric value. For large ( ¾Û ½ ) the number is converted to a negative value. To summarize, we can consider the effects of converting in both directions between unsigned and two’s Û ½ complement representations. For values in the range ¼ Ü ¾ we have Ì¾Í Û ´Üµ Ü and Í¾Ì Û ´Üµ Ü. That is, numbers in this range have i...
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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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