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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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