Assembly print hex

print_hex.asm

[org 0x7c00]

  mov dx, 0x1fb7    ; Set the value we want to print to dx
  call print_hex    ; Print the hex value
  jmp $             ; Hang once we're done

%include "print_string.asm"

; Prints the value of DX as hex.
print_hex:
  pusha             ; save the register values to the stack for later

  mov cx,4          ; Start the counter: we want to print 4 characters
                    ; 4 bits per char, so we're printing a total of 16 bits

char_loop:
  dec cx            ; Decrement the counter

  mov ax,dx         ; copy bx into ax so we can mask it for the last chars
  shr dx,4          ; shift bx 4 bits to the right
  and ax,0xf        ; mask ah to get the last 4 bits

  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,0xa        ; Check to see if it's a letter or number
  jl set_letter     ; If it's a number, go straight to setting the value
  add byte [bx],7   ; If it's a letter, add 7
                    ; Why this magic number? ASCII letters start 17
                    ; characters after decimal numbers. We need to cover that
                    ; distance. If our value is a 'letter' it's already
                    ; over 10, so we need to add 7 more.
  jl set_letter

set_letter:
  add byte [bx],al  ; Add the value of the byte to the char at bx

  cmp cx,0          ; check the counter, compare with 0
  je print_hex_done ; if the counter is 0, finish
  jmp char_loop     ; otherwise, loop again

print_hex_done:
  mov bx, HEX_OUT   ; print the string pointed to by bx
  call print_string

  popa              ; pop the initial register values back from the stack
  ret               ; return the function

; global variables
HEX_OUT: db '0x0000',0

; Padding and magic number

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

print_string.asm

print_string:     ; Push registers onto the stack
  pusha

string_loop:
  mov al, [bx]    ; Set al to the value at bx
  cmp al, 0       ; Compare the value in al to 0 (check for null terminator)
  jne print_char  ; If it's not null, print the character at al
                  ; Otherwise the string is done, and the function is ending
  popa            ; Pop all the registers back onto the stack
  ret             ; return execution to where we were

print_char:
  mov ah, 0x0e    ; Linefeed printing
  int 0x10        ; Print character
  add bx, 1       ; Shift bx to the next character
  jmp string_loop ; go back to the beginning of our loop

Greetings,
I am new to assembly and I was trying to figure this out, however it seems to me this code skips the first nibble and immediately goes to right shift...
Could someone more knowledgeable than me give me some insight?
Thanks!

p.s. I've already written this code differently and it works without affecting the initial HEX_OUT, I'm asking out of curiosity because I don't want to miss something in this early stage of learning asm...

I have updated the function here https://gist.github.com/kthompson/957c635d84b7813945aa9bb649f039b9 so that it is not required to reset the HEX_OUT variable each time.