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| Teaching Since: | May 2017 |
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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
[M] The 1’s-complement and 2’s-complement binary representation methods are special cases of the (b − 1)’s-complement and b’s-complement representation techniques in base b number systems. For example, consider the decimal system. The sign-and-magnitude values +526, −526, +70, and −70 have 4-digit signed-number representations in each of the two complement systems, as shown in Figure P9.1. The 9’s-complement is formed by taking the complement of each digit position with respect to 9. The 10’s-complement is formed by adding 1 to the 9’s-complement. In each of the latter two representations, the leftmost digit is zero for a positive number and 9 for a negative number. Now consider the base-3 (ternary) system, in which the unsigned, 5-digit number t4t3t2t1t0 has the value t4 × 34 + t3 × 33 + t2 × 32 + t1 × 31 + t0 × 30, with 0 ≤ ti ≤ 2. Express the ternary sign-and-magnitude numbers +11011, −10222, +2120, −1212, +10, and −201 as 6-digit, signed, ternary numbers in the 3’s-complement system.

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