format mz
entry code:start

segment datas
                buff dd 0
                strs db "0123456789ABCDEF"
                string db " >>> is eax value$"
segment code
                start:
                        mov ax,datas
                        mov ds,ax
                        push ax                                 ;save data
                        xchg ah,al                                      ;swaps
                        call printf                                     ;call print
                        pop ax                                  ;pop data
                        call printf
                        call print
                        mov ax,4c00h
                        int 21h

printf:
                        xor ah,ah                                       ;zero setting 
                        xor bx,bx
                        mov bl,16
                        div bl                                          ;In addition to the 10 
                        mov bl,al
                        mov byte[buff],ah                       ;save buff
                        mov dl,[strs+bx]                        ;seach string array
                        mov ah,2
                        int 21h
                        mov bl,byte[buff]
                        mov dl,[strs+bx]
                        mov ah,2
                        int 21h
                        ret
print:
                        lea dx,[string]
                        mov ah,9
                        int 21h
                        ret

    

D:\try>debug n39.exe
-g
0BA1 >>> is eax value
Program terminated normally

There's no reason to need "div" by any power of 2 (e.g. 16), you can use a shift instead.

Anyways, this kind of exercise is always interesting, but of course it's been done before: https://board.flatassembler.net/topic.php?t=7109