#: Antibase 2 - Antibase

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Antibase Two #: _ 1 0 Antibase

#: y is the binary representation of y , and is equivalent to (m#2)#:y ,where m is the maximum of the number of digits needed to represent the atoms of y in base 2 .For example:

 i. 8
0 1 2 3 4 5 6 7
 
 #: i. 8
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

In simple cases r&#: is inverse to r&#. . Thus:

 r=: 24 60 60
 r #: r #. 2 3 4
2 3 4

But if r #. y exceeds (*/r)-1 (the largest integer representable in the radix r), then the result of r#:y is reduced modulo */r . For example:

 r #: r #. 29 3 4
5 3 4

A representation in an arbitrary base that is analogous to the base-2 representation provided by the monadic use of #: may be provided as illustrated below:

 ndr=: 1 + <.@^. Number of digits required
 10 ndr y=: 9 10 11 100 99 100
1 2 2 3 2 3
 (y#:~10 #~ >./10 ndr y);(y#:~8 #~ >./8 ndr y)
+-----+-----+
|0 0 9|0 1 1|
|0 1 0|0 1 2|
|0 1 1|0 1 3|
|1 0 0|1 4 4|
|0 9 9|1 4 3|
|1 0 0|1 4 4|
+-----+-----+
 (10&#.^:_1 ; 8&#.^:_1) y
+-----+-----+
|0 0 9|0 1 1|
|0 1 0|0 1 2|
|0 1 1|0 1 3|
|1 0 0|1 4 4|
|0 9 9|1 4 3|
|1 0 0|1 4 4|
+-----+-----+

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