Another approach to convert an unsigned integer to a string and write it:
section .text
global _start
_start:
mov eax, 1234567890
mov ebx, 5
add eax, ebx
; Convert EAX to ASCII and store it onto the stack
sub esp, 16 ; reserve space on the stack
mov ecx, 10
mov ebx, 16
.L1:
xor edx, edx ; Don't forget it!
div ecx ; Extract the last decimal digit
or dl, 0x30 ; Convert remainder to ASCII
sub ebx, 1
mov [esp+ebx], dl ; Store remainder on the stack (reverse order)
test eax, eax ; Until there is nothing left to divide
jnz .L1
mov eax, 4 ; SYS_WRITE
lea ecx, [esp+ebx] ; Pointer to the first ASCII digit
mov edx, 16
sub edx, ebx ; Count of digits
mov ebx, 1 ; STDOUT
int 0x80 ; Call 32-bit Linux
add esp, 16 ; Restore the stack
mov eax, 1 ; SYS_EXIT
xor ebx, ebx ; Return value
int 0x80 ; Call 32-bit Linux