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plurals

PO
primarykey
Id
7876362
data
AcceptedAnswerId
0
AnswerCount
0
ClosedDate
CommentCount
0
CommunityOwnedDate
CreationDate
2011-10-24T13:30:04.183
FavoriteCount
0
LastActivityDate
2012-09-24T11:59:51.330
LastEditDate
2012-09-24T11:59:51.330
LastEditorUserId
253056
OwnerUserId
253056
ParentId
7876351
PostTypeId
2
Score
16
ViewCount
0
LastEditorDisplayName
text
Body
This only works for powers of 2. In general: <pre><code>x MOD 2^n </code></pre> is equivalent to: <pre><code>x AND (2^n - 1) </code></pre> Note also that this may be true only for <code>x >= 0</code>, depending on your definition of <code>MOD</code> for <code>x < 0</code>. <hr> To understand why this works, consider what MOD really is - it's just the remainder after performing integer division. In the case of a division by 2^n, we are effectively just shifting a binary value right by n bits and discarding any low order bits that get shifted out, e.g. for an 8 bit binary number <pre><code>a b c d e f g h </code></pre> if we divide by 4 = 2^2 then we shift right by 2 bits: <pre><code>0 0 a b c d e f </code></pre> The remainder (<code>g h</code>) has been thrown away as a result of the integer division. If we wanted to know the remainder then we could just extract the bits <code>g h</code> by applying a mask of <code>0 0 0 0 0 0 1 1</code>: <pre><code> a b c d e f g h AND 0 0 0 0 0 0 1 1 = 0 0 0 0 0 0 g h </code></pre> Note that the has has value 3, which in the general case is just 2^n - 1. Let's try this with some real numbers. Suppose we want to calculate 42 / 4 and get both the quotient and the remainder: <pre><code>42 = 0 0 1 0 1 0 1 0 </code></pre> To get the quotient we shift right by 2 bits: <pre><code> 42 / 4 (decimal) = 0 0 1 0 1 0 1 0 >> 2 = 0 0 0 0 1 0 1 0 = 10 (decimal) 42 MOD 4 (decimal) = 0 0 1 0 1 0 1 0 AND 0 0 0 0 0 0 1 1 = 0 0 0 0 0 0 1 0 = 2 (decimal) </code></pre> So 42/4 = 10 remainder 2.
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singulars
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1. This table or related slice is empty.
PostParentId
1. POWhy is ( x & 3 ) identical to ( x mod 4 )?
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 PTQuestion
PostTypePostTypeId
1. PTAnswer
UserLastEditorUserId
1. USPaul R
UserOwnerUserId
1. USPaul R
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1. VO
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 VTUpMod
2. VO
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3. VO
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1. This table or related slice is empty.

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