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 Boolean m b.  _ 0 0

 The monad is equivalent to a zero left argument; that is, m b. y ↔ 0 m b. y If f is a dyadic boolean function and d=: 0 1 , then d f/ d (or f/~d) is its complete table. For example the tables for or, nor, and, and not-and appear as follows: ``` (+./~ ; +:/~ ; *./~ ; *:/~) d=: 0 1 +---+---+---+---+ |0 1|1 0|0 0|1 1| |1 1|0 0|0 1|1 0| +---+---+---+---+ ``` If ordered by their tables, each of the sixteen possible boolean dyads can be characterized by its index k ; the phrase k b. produces the corresponding function. Moreover, negative indexing and array arguments may be used. An atom m=16+k specifies bitwise boolean functions on integer arguments. An argument atom is treated as a list of length w of bits, where w is the word size of the underlying machine. For example, 17 b. specifies bitwise and. Finally, 32 b. specifies rotate, 33 b. specifies shift, and 34 b. specifies signed shift.

The following table lists all the possible boolean functions:
 m RavelledTable Function 0 _16 16 0 0 0 0 0 1 _15 17 0 0 0 1 x *. y 2 _14 18 0 0 1 0 x > y 3 _13 19 0 0 1 1 x 4 _12 20 0 1 0 0 x < y 5 _11 21 0 1 0 1 y 6 _10 22 0 1 1 0 x ~: y 7 _9 23 0 1 1 1 x +. y 8 _8 24 1 0 0 0 x +: y 9 _7 25 1 0 0 1 x = y 10 _6 26 1 0 1 0 -. y 11 _5 27 1 0 1 1 x >: y 12 _4 28 1 1 0 0 -. x 13 _3 29 1 1 0 1 x <: y 14 _2 30 1 1 1 0 x *: y 15 _1 31 1 1 1 1 1 32 rotate 33 shift 34 signed shift

Further examples:
```   (7 b./~ ; 8 b./~ ; 1 b./~ ; 14 b./~) d=: 0 1
+---+---+---+---+
|0 1|1 0|0 0|1 1|
|1 1|0 0|0 1|1 0|
+---+---+---+---+

(_1 b./~ ; _3 b./~ ; _15 b./~) d       NB. negative indexing
+---+---+---+
|1 1|1 1|0 0|
|1 1|0 1|0 1|
+---+---+---+

(<"2) 2 0 1 |: 7 8 1 15 b./~ d         NB. array arguments
+---+---+---+---+
|0 1|1 0|0 0|1 1|
|1 1|0 0|0 1|1 1|
+---+---+---+---+

12345 (17 b.) 67890                    NB. bitwise and
48
f=: (32#2)&#: { '.x'"_
f 12345 67890 48
..................xx......xxx..x
...............x....x..x..xx..x.
..........................xx....

_12345 (23 b.) 67890                   NB. bitwise or
_12297
f _12345 67890 _12297
xxxxxxxxxxxxxxxxxx..xxxxxx...xxx
...............x....x..x..xx..x.
xxxxxxxxxxxxxxxxxx..xxxxxxxx.xxx

20 b./~ i.10                           NB. bitwise less than table
0 1 2 3 4 5 6 7 8 9
0 0 2 2 4 4 6 6 8 8
0 1 0 1 4 5 4 5 8 9
0 0 0 0 4 4 4 4 8 8
0 1 2 3 0 1 2 3 8 9
0 0 2 2 0 0 2 2 8 8
0 1 0 1 0 1 0 1 8 9
0 0 0 0 0 0 0 0 8 8
0 1 2 3 4 5 6 7 0 1
0 0 2 2 4 4 6 6 0 0

23 b./\ 2^i.10                         NB. cumulative bitwise or
1 3 7 15 31 63 127 255 511 1023

_5 (33 b.) 12345                       NB. shift
385
f 12345 385
..................xx......xxx..x
.......................xx......x

_5 (33 b.) _12345                      NB. shift
134217342
f _12345 134217342
xxxxxxxxxxxxxxxxxx..xxxxxx...xxx
.....xxxxxxxxxxxxxxxxxx..xxxxxx.

_5 (34 b.) _12345                      NB. signed shift
_386
f _12345 _386
xxxxxxxxxxxxxxxxxx..xxxxxx...xxx
xxxxxxxxxxxxxxxxxxxxxxx..xxxxxx.

```

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