14 it is well known that modular arithmetic forms a

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Unformatted text preview: Û ½) and obtained a nonnegative result Þ¼¼ Ü · Ý · ¾Û . ½ . Then we will have Þ ¼ Þ · ¾ . This gives ¼ Þ ¼ ¾ ½ · ¾ ½ . ¾ ¼ is in the range such that Þ ¼¼ Þ ¼ . This case is referred to as Examining Equation 2.6, we see that Þ ¾ Û Þ ¾ Û Û Û Û Û ½ Þ ¼ 3. ½ . Then we will have Þ ¼ Þ , giving ¼ Þ ¼ two’s complement sum Þ ¼¼ equals the integer sum Ü · Ý . Þ ¾ Û ¾ Û ½ , and hence Þ ¼¼ Þ¼ Þ . Again, the 58 CHAPTER 2. REPRESENTING AND MANIPULATING INFORMATION Ü Ý Ü · Ý Ü +t Ý ½¿ ¿ ¼¼½½ Case 1 1 2 3 ½¼¼¼ ½¼½½ ½ ¼ ¼¼¼¼ ¿ ½¼¼¼ ½¼¼¼ ¿ ½¼¼¼ ¾ ¼¼½¼ ¼½¼½ ½½¼½ ¼½¼½ ½¼ ¼½½½ 4 ¼½¼½ ¼½¼½ ½¼½¼ Figure 2.18: Two’s Complement Addition Examples. The bit-level representation of the four-bit two’s complement sum can be obtained by performing binary addition of the operands and truncating the result to bits. 4. . We will again have Þ ¼ Þ , giving ¾Û ½ Þ ¼ ¾Û . But in this range we have Þ ¼¼ Þ ¼ ¾Û , giving Þ ¼...
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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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