print numberic value from given register as hex on the screen

hex_to_string.asm

; Super highly inspired by https://gist.github.com/kthompson/957c635d84b7813945aa9bb649f039b9
[org 0x7c00]  

mov dx, 0x1fb6 ; set function argument
call print_hex ; call the function

jmp $

; arg0: dx - numeric value to be printed in hexdecimal format
print_hex:
  pusha ;
  mov cx, 4 ; we are in 16bit mode, so our 16bit value has 4 * 4bytes (4bytes = one char)
  mov bx, HEX_OUT
  add bx, 2 ; skip '0x' charactes

  char_loop:
  dec cx
  mov ax, dx
  shr dx, 4
  and ax, 0xf

  mov bx, HEX_OUT   ; set bx to the memory address of our string
  add bx, 2         ; skip the '0x'
  add bx, cx        ; add the current counter to the address
 
  cmp ax, 9
  jle numeric
  jmp character

  character:
  sub ax, 10
  add ax, 97
  jmp add_letter

  numeric:
  add ax, 48
  jmp add_letter

  add_letter:
  mov byte [bx], al

  cmp cx, 0
  je done
  jmp char_loop

  done:
  call print_string
  popa
  ret


; arg0: bx - pointer to string to be printed
print_string:
  pusha
  iteration:
  mov cx, [bx]
  cmp cl, 0
  je end
  ; print character
  mov al, cl
  mov ah, 0x0e
  int 0x10
  ; increment string pointer
  add bx, 1
  jmp iteration
  end:
  popa
  ret

HEX_OUT: db '0x0000', 0

times 510-($-$$) db 0
dw 0xaa55