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plurals

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12953182
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0
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2012-10-18T11:06:00.207
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2012-10-18T11:06:00.207
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5
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End-around carry is actually rather simple: it changes the modulus of the addition operation from rn to rn–1, if you think of the numbers as unsigned. To simplify things, let's talk about binary. Let's compute (-2) + (-4) using four-bit two's complement arithmetic: <pre> 1 1 1 0 (-2) + 1 1 0 0 + (-4) --------- ------ 1 1 0 1 0 (-6) </pre> Let's keep the carry bit where it is for now. If you look at the numbers as unsigned integers, we're computing 14 + 12 = 26. However, addition is done modulo 16, so we get 10, which is the unsigned number which represents -6 (the correct result). In ones' complement, the numbers have different representations: <pre> 1 1 0 1 (-2) + 1 0 1 1 + (-4) --------- ------ 1 1 0 0 0 (-6) </pre> Again, let's keep the carry bit where it is. If you look at the numbers as unsigned integers, we're computing 13 + 11 = 24. However, due to the wrap-around carry, addition is done modulo 15, so we end up with 9, which represents -6 (the correct result). So in four-bit two's complement, -2 is equivalent to 14 modulo 16, -4 is equivalent to 12 modulo 16, and -6 is equivalent to 10 modulo 16. And in four-bit ones' complement, -2 is equivalent to 13 modulo 15, -4 is equivalent to 11 modulo 15, and -6 is equivalent to 9 modulo 15. Signed zero: The reason you get "signed zero" is because there are 16 possible numbers in four bit, but if you're doing modulo-15 arithmetic, then 0 and 15 are equivalent. That's all there is to it.
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1. This table or related slice is empty.
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1. POReason for end around carry to do
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1. USDietrich Epp
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1. POReason for end around carry to do
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1. COThank you!Now I have more understand it!
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