8.28 Binary & Representation Of Numbers

Signmagnitudeuseanextrabitfor 51010101 51011101

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Unformatted text preview: atch?v=GcDshWmhF4A Binary Subtraction Decimal Subtraction Binary Subtraction 8423 6915 ­­­­­­­­­­ 1101011 1001101 ­­­­­­­­­­­ ..wait.. What about 1001101 – 1101011? How do we represent negative numbers? Properties of a Properties of a Good Representation Should be simple Allows us to do useful things Should be efficient Recovering from errors should be possible Negative Numbers Negative Numbers How would we represent ­5 in binary? Sign­magnitude: use an extra bit for +/­ + 5 = (+) 101 = 0101 ­ 5 = (­) 101 = 1101 (this assumes we have a fixed (known) word size so that we know the first bit represents +/­, and not the next power of 2) What about 0? – different 0’s can cause problems Negative Numbers Negative Numbers Sign­magnitude (use one bit for sign) is perfectly acceptable, with minor inconvenience, but is not as good as a clever alternative. “Two’s complement notation” is used. – – – only one representation of 0 allows computation of subtraction via addition a bit confusing on first sight. Towards understanding two’s complement: Towards understanding two Using 1 digit Suppose we had the symbols 0 through 9. How many (positive and negative) numbers can we represent? Which symbol gets which number? 10’s complement 10 0 ­1 ­2 ­3 9 8 0 1 1 7 ­4 3 5 ­5 4 2 2 repr...
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This document was uploaded on 04/02/2014.

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