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Unformatted text preview: When Ü ¼, the additive inverse is clearly ¼. For Û Û Û Ü ¼, consider the value ¾Û Ü. Observe that this number is in the range ¼ ¾Û Ü ¾Û , and Û ´Ü · ¾ Üµ ÑÓ ¾Û ¾Û ÑÓ ¾Û ¼. Hence it is the inverse of Ü under +uÛ . These two cases lead to the following equation for ¼ Ü ¾Û : -u Ü Û Practice Problem 2.17:
We can represent a bit pattern of length Û with a single hex digit. For an unsigned interpretation of these digits use Equation 2.10 ﬁll in the following table giving the values and the bit representations (in hex) of the unsigned additive inverses of the digits shown.
Ü ´ Ü
Û Ü Ü Ü ¼ ¼ (2.10) -u Decimal Decimal Ü Hex 0 3 8 A F Hex 2.3.2 Two’s Complement Addition
A similar problem arises for two’s complement addition. Given integer values Ü and Ý in the range ¾Û ½ Ü Ý ¾Û ½ ½, their sum is in the range ¾Û Ü · Ý ¾Û ¾, potentially requiring Û · ½ bits to represent exactly. As before, we avoid ever-expanding data sizes b...
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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