TASM string to hexadecimal number - string

Question

I have a problem with a TASM based assembly code. I would like to convert a string in the "string" pointer into a decimal number and then print it as a hexadecimal one. However the code prints only the first 2 characters from the right correctly. What may be wrong with this?
concd SEGMENT
ASSUME cs: concd
ORG 100h
main:
mov ax, 0
mov bx, offset string
mov cx, 0
mov dx, 0
mov si, 0
jump:
mov cx, [bx + si]
cmp cx, 0h ;checking if we reached the end of the string
jz exit
mov dx, ax
mov cx, 9
mult:
add ax, dx ;loop for multiplying by 10
loop mult
mov cx, [bx + si]
sub cx, 30h
add ax, cx
inc si
jmp jump
exit:
call hex
mov ah, 04Ch
mov al, 0
int 21h
hex PROC
mov dx, ax
mov cl, 12
jump2:
mov ax, dx
shr ax, cl
and ax, 15
cmp ax, 9
jng t
add ax, 7h
t: add ax, 30h
call putc
sub cl, 4
jnc jump2
RET
hex ENDP
putc PROC
mov ah, 0Eh
int 10h
RET
putc ENDP
string DB "1234", 0h
concd ENDS
END main

Answer 1

I made some small changes, and now it works.
I commented with "phase 1" the changes that it actually did get a character abd did something, and with "phase 2" the changes that corrected the conversion.
Now it's OP's time to figure out what was wrong.
concd SEGMENT
ASSUME cs: concd
ORG 100h
main:
mov ax, cs ;; added - phase 1
mov ds, ax ;; added - phase 1
mov ax, 0
mov bx, offset string
mov cx, 0
mov dx, 0
mov si, 0
jump:
mov ch, 0 ;; Added - phase 2
mov cl, [bx + si] ;; added - phase 2
;mov cx, [bx + si] ;; removed - phase 2
cmp cx, 0h ;checking if we reached the end of the string
jz exit
mov dx, ax
mov cx, 9
mult: ; ax contains the number
;; removed the next 2 lines - phase 2
;add ax, dx ;loop for multiplying by 10
;loop mult
;; added the next 2 lines - phase 2
mov cl, 10
mul cl ; multiply by 10
mov cx, [bx + si]
sub cx, 30h
add ax, cx
inc si
jmp jump
exit:
call hex
mov ah, 04Ch
mov al, 0
int 21h
hex PROC
mov dx, ax
mov cl, 12
jump2:
mov ax, dx
shr ax, cl
and ax, 15
cmp ax, 9
jng t
add ax, 7h
t: add ax, 30h
call putc
sub cl, 4
jnc jump2
RET
hex ENDP
putc PROC
mov ah, 0Eh
int 10h
RET
putc ENDP
string DB "1234", 0h
concd ENDS
END main