Convert a number to Hexadecimal

Turing Machine Code, 412 bytes

As usual, I'm using the rule table syntax defined here. You can test it on that site or, alternatively, using this java implementation.

0 * * l B
B * * l C
C * 0 r D
D * * r E
E * * r A
A _ * l 1
A * * r *
1 0 9 l 1
1 1 0 l 2
1 2 1 l 2
1 3 2 l 2
1 4 3 l 2
1 5 4 l 2
1 6 5 l 2
1 7 6 l 2
1 8 7 l 2
1 9 8 l 2
1 _ * r Y
Y * * * X
X * _ r X
X _ _ * halt
2 * * l 2
2 _ _ l 3
3 * 1 r 4
3 1 2 r 4
3 2 3 r 4
3 3 4 r 4
3 4 5 r 4
3 5 6 r 4
3 6 7 r 4
3 7 8 r 4
3 8 9 r 4
3 9 A r 4
3 A B r 4
3 B C r 4
3 C D r 4
3 D E r 4
3 E F r 4
3 F 0 l 3
4 * * r 4
4 _ _ r A

Counts down from the input in base 10 while counting up from 0 in base 16. On decrementing zero, it erases the input block and terminates.

Java, 92 89 bytes

String x(int v){String z="";for(;v>0;v/=16)z="0123456789ABCDEF".charAt(v%16)+z;return z;}

Javascript, 49 43 bytes.

h=i=>(i?h(i>>4):0)+"0123456789abcdef"[i%16]

6 bytes saved by user81655.

Test it here.

This has two leading zeroes, which is allowed by the rules.

Here's a version without leading zeroes: (47 bytes).

h=i=>(i>15?h(i>>4):"")+"0123456789abcdef"[i%16]

Test it here.

Both of these uses exactly the same approach as my Python answer.