```cvex ←    {width} ##.hex nums               ⍝ Hexadecimal from decimal.
nums ← {signed←0} ##.dec cvex               ⍝ Decimal from hexadecimal.

[hex] and [dec] convert between arrays of decimal numbers and their  hexadecimal
equivalents.

Hex's optional left argument {width} specifies the number of  hexadecimal digits
required. Width defaults to 2, 4, 8 or 16 depending on the magnitude of the arg-
ument.

Dec's optional left argument {signed} determines whether  a  hexadecimal  number
whose first digit is in the range 8..f is to  be interpreted as a signed or  un-
signed (default) number.

Restriction: [hex] will not accept numbers whose magnitude means  that  adding 1
will make no difference: a maximum of around 2*53 for a number of ⎕DR-type 645.

Examples:

hex 12 34 56                            ⍝ (result is nested).
┌──┬──┬──┐
│0c│22│38│
└──┴──┴──┘

hex 100×⍳6                              ⍝ larger numbers.
┌────┬────┬────┬────┬────┬────┐
│0064│00c8│012c│0190│01f4│0258│
└────┴────┴────┴────┴────┴────┘

hex 100000×⍳4                           ⍝ even larger numbers.
┌────────┬────────┬────────┬────────┐
│000186a0│00030d40│000493e0│00061a80│
└────────┴────────┴────────┴────────┘

hex 4 5⍴⍳20                             ⍝ array of numbers.
┌──┬──┬──┬──┬──┐
│01│02│03│04│05│
├──┼──┼──┼──┼──┤
│06│07│08│09│0a│
├──┼──┼──┼──┼──┤
│0b│0c│0d│0e│0f│
├──┼──┼──┼──┼──┤
│10│11│12│13│14│
└──┴──┴──┴──┴──┘

4 hex 4 5⍴⍳20                           ⍝ specify width.
┌────┬────┬────┬────┬────┐
│0001│0002│0003│0004│0005│
├────┼────┼────┼────┼────┤
│0006│0007│0008│0009│000a│
├────┼────┼────┼────┼────┤
│000b│000c│000d│000e│000f│
├────┼────┼────┼────┼────┤
│0010│0011│0012│0013│0014│
└────┴────┴────┴────┴────┘

dec 'ace' 'ACE'                         ⍝ upper and lower case accepted
2766 2766

dec hex 2 4 5⍴⍳40                       ⍝ convert both ways.
1  2  3  4  5
6  7  8  9 10
11 12 13 14 15
16 17 18 19 20

21 22 23 24 25
26 27 28 29 30
31 32 33 34 35
36 37 38 39 40

hex saw(1 2 3)(100 200 300)             ⍝ nested array.
┌──────────┬────────────────┐
│┌──┬──┬──┐│┌────┬────┬────┐│
││01│02│03│││0064│00c8│012c││
│└──┴──┴──┘│└────┴────┴────┘│
└──────────┴────────────────┘

dec hex (1 2 3)(100 200 300)            ⍝ full circle.
┌─────┬───────────┐
│1 2 3│100 200 300│
└─────┴───────────┘

⍝ hex of negative integers returns 2's complement or "unsigned" hex number:

hex ¯3 to 3                             ⍝ hex of negative numbers.
┌──┬──┬──┬──┬──┬──┬──┐
│fd│fe│ff│00│01│02│03│
└──┴──┴──┴──┴──┴──┴──┘

1 dec hex ¯3 to 3                       ⍝ round trip if signed.
¯3 ¯2 ¯1 0 1 2 3

0 dec hex ¯3 to 3                       ⍝ non-round trip if unsigned.
253 254 255 0 1 2 3

hex 2*53                                ⍝ number too big.
Too big
hex 2*53
∧