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Unformatted text preview: Ý are negative, t but Ü +tÛ Ý ¼, we have negative overﬂow. When both Ü and Ý are positive, but Ü +Û Ý ¼, we have positive overﬂow. Practice Problem 2.18: As an illustration, Figure 2.18 shows some examples of four-bit two’s complement addition. Each example is labeled by the case to which it corresponds in the derivation of Equation 2.12. Note that ¾ ½ , and hence negative overﬂow yields a result 16 more than the integer sum, and positive overﬂow yields a result 16 less. We include bit-level representations of the operands and the result. Observe that the result can be obtained by performing binary addition of the operands and truncating the result to four bits. 2.3. INTEGER ARITHMETIC 59 Two's Complement Addition (4-bit word) 8 6 4 2 0 -2 -4 -6 -8 Negative Overflow Normal Positive Overflow 6 4 2 0 -2 -8 -4 -6 -4 -2 -6 0 2 4 -8 6 Figure 2.19: Two’s Complement Addition. With a four-bit word size, addition can have a negative overﬂow when Ü · Ý and a positive overﬂow when Ü · Ý . 60 CHAPTER 2. REPRESENTING AND MANIPULATING INFORMATION
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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