Class Note for ECE 369 at UA
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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 18 views.
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Date Created: 02/06/15
OVERFLOW When adding numbers together using the 239s complement notation Add the numbers together in the usual way as if they are just normal binary numbers When dealing with 239s complement any bit pattern that has a sign bit of zero in other words a positive number is just the same as a normal binary number you don39t need to convert it back out of 239s complement in any way just convert it straight into decimal as you would convert a normal binary numberlf on the other hand the sign bit is 1 this means that the corresponding decimal number is negative and the bit pattern needs to be converted out of 239s complement before you can convert it from binary into decimalLook at the 239s complement tables below notice how all numbers from zero upwards are exactly the same as the usual binary representation for each value Only the negative values ie all those bit patterns starting with a 1 do not correspond to the usual binary representation so they have to be converted from 239s complement notation into normal binary before we can then convert them from binary to decimal Two39s complement using patterns of length 3 and 4 are WW Tlf Tlf 001 1 000 W Tlf Tlf TIT TIT If an addition operation produces a result that exceeds the range of the number system overflow is said to occur In the modular counting representation shown above overflow occurs during the addition of positive numbers when we count past 7 Addition of two numbers with different signs can never produce overflow but addition of two numbers of like sign can as shown by the following examples mi Wi 0101 Wi 0011 Wi Wi Wi ij WW WW ij ij TjT W WW O MQJLU ICD 3 1101 5 0101 6 1010 6 0110 9 101117 11 10115 8 1000 7 0111 8 1000 7 0111 16 100000 14 11102