Suppose that I have an integer number in a register, how can I print it? Can you show a simple example code?
I already know how to print a string such as "hello, world".
I'm developing on Linux.
If you're already on Linux, there's no need to do the conversion yourself. Just use printf instead:
;
; assemble and link with:
; nasm -f elf printf-test.asm && gcc -m32 -o printf-test printf-test.o
;
section .text
global main
extern printf
main:
mov eax, 0xDEADBEEF
push eax
push message
call printf
add esp, 8
ret
message db "Register = %08X", 10, 0
Note that printf uses the cdecl calling convention so we need to restore the stack pointer afterwards, i.e. add 4 bytes per parameter passed to the function.
You have to convert it in a string; if you're talking about hex numbers it's pretty easy. Any number can be represented this way:
0xa31f = 0xf * 16^0 + 0x1 * 16^1 + 3 * 16^2 + 0xa * 16^3
So when you have this number you have to split it like I've shown then convert every "section" to its ASCII equivalent.
Getting the four parts is easily done with some bit magic, in particular with a right shift to move the part we're interested in in the first four bits then AND the result with 0xf to isolate it from the rest. Here's what I mean (soppose we want to take the 3):
0xa31f -> shift right by 8 = 0x00a3 -> AND with 0xf = 0x0003
Now that we have a single number we have to convert it into its ASCII value. If the number is smaller or equal than 9 we can just add 0's ASCII value (0x30), if it's greater than 9 we have to use a's ASCII value (0x61).
Here it is, now we just have to code it:
mov si, ??? ; si points to the target buffer
mov ax, 0a31fh ; ax contains the number we want to convert
mov bx, ax ; store a copy in bx
xor dx, dx ; dx will contain the result
mov cx, 3 ; cx's our counter
convert_loop:
mov ax, bx ; load the number into ax
and ax, 0fh ; we want the first 4 bits
cmp ax, 9h ; check what we should add
ja greater_than_9
add ax, 30h ; 0x30 ('0')
jmp converted
greater_than_9:
add ax, 61h ; or 0x61 ('a')
converted:
xchg al, ah ; put a null terminator after it
mov [si], ax ; (will be overwritten unless this
inc si ; is the last one)
shr bx, 4 ; get the next part
dec cx ; one less to do
jnz convert_loop
sub di, 4 ; di still points to the target buffer
PS: I know this is 16 bit code but I still use the old TASM :P
PPS: this is Intel syntax, converting to AT&T syntax isn't difficult though, look here.
Linux x86-64 with printf
main.asm
default rel ; make [rel format] the default, you always want this.
extern printf, exit ; NASM requires declarations of external symbols, unlike GAS
section .rodata
format db "%#x", 10, 0 ; C 0-terminated string: "%#x\n"
section .text
global main
main:
sub rsp, 8 ; re-align the stack to 16 before calling another function
; Call printf.
mov esi, 0x12345678 ; "%x" takes a 32-bit unsigned int
lea rdi, [rel format]
xor eax, eax ; AL=0 no FP args in XMM regs
call printf
; Return from main.
xor eax, eax
add rsp, 8
ret
GitHub upstream.
Then:
nasm -f elf64 -o main.o main.asm
gcc -no-pie -o main.out main.o
./main.out
Output:
0x12345678
Notes:
sub rsp, 8: How to write assembly language hello world program for 64 bit Mac OS X using printf?
xor eax, eax: Why is %eax zeroed before a call to printf?
-no-pie: plain call printf doesn't work in a PIE executable (-pie), the linker only automatically generates a PLT stub for old-style executables. Your options are:
call printf wrt ..plt to call through the PLT like traditional call printf
call [rel printf wrt ..got] to not use a PLT at all, like gcc -fno-plt.
Like GAS syntax call *printf#GOTPCREL(%rip).
Either of these are fine in a non-PIE executable as well, and don't cause any inefficiency unless you're statically linking libc. In which case call printf can resolve to a call rel32 directly to libc, because the offset from your code to the libc function would be known at static linking time.
See also: Can't call C standard library function on 64-bit Linux from assembly (yasm) code
If you want hex without the C library: Printing Hexadecimal Digits with Assembly
Tested on Ubuntu 18.10, NASM 2.13.03.
It depends on the architecture/environment you are using.
For instance, if I want to display a number on linux, the ASM code will be different from the one I would use on windows.
Edit:
You can refer to THIS for an example of conversion.
I'm relatively new to assembly, and this obviously is not the best solution,
but it's working. The main function is _iprint, it first checks whether the
number in eax is negative, and prints a minus sign if so, than it proceeds
by printing the individual numbers by calling the function _dprint for
every digit. The idea is the following, if we have 512 than it is equal to: 512 = (5 * 10 + 1) * 10 + 2 = Q * 10 + R, so we can found the last digit of a number by dividing it by 10, and
getting the reminder R, but if we do it in a loop than digits will be in a
reverse order, so we use the stack for pushing them, and after that when
writing them to stdout they are popped out in right order.
; Build : nasm -f elf -o baz.o baz.asm
; ld -m elf_i386 -o baz baz.o
section .bss
c: resb 1 ; character buffer
section .data
section .text
; writes an ascii character from eax to stdout
_cprint:
pushad ; push registers
mov [c], eax ; store ascii value at c
mov eax, 0x04 ; sys_write
mov ebx, 1 ; stdout
mov ecx, c ; copy c to ecx
mov edx, 1 ; one character
int 0x80 ; syscall
popad ; pop registers
ret ; bye
; writes a digit stored in eax to stdout
_dprint:
pushad ; push registers
add eax, '0' ; get digit's ascii code
mov [c], eax ; store it at c
mov eax, 0x04 ; sys_write
mov ebx, 1 ; stdout
mov ecx, c ; pass the address of c to ecx
mov edx, 1 ; one character
int 0x80 ; syscall
popad ; pop registers
ret ; bye
; now lets try to write a function which will write an integer
; number stored in eax in decimal at stdout
_iprint:
pushad ; push registers
cmp eax, 0 ; check if eax is negative
jge Pos ; if not proceed in the usual manner
push eax ; store eax
mov eax, '-' ; print minus sign
call _cprint ; call character printing function
pop eax ; restore eax
neg eax ; make eax positive
Pos:
mov ebx, 10 ; base
mov ecx, 1 ; number of digits counter
Cycle1:
mov edx, 0 ; set edx to zero before dividing otherwise the
; program gives an error: SIGFPE arithmetic exception
div ebx ; divide eax with ebx now eax holds the
; quotent and edx the reminder
push edx ; digits we have to write are in reverse order
cmp eax, 0 ; exit loop condition
jz EndLoop1 ; we are done
inc ecx ; increment number of digits counter
jmp Cycle1 ; loop back
EndLoop1:
; write the integer digits by poping them out from the stack
Cycle2:
pop eax ; pop up the digits we have stored
call _dprint ; and print them to stdout
dec ecx ; decrement number of digits counter
jz EndLoop2 ; if it's zero we are done
jmp Cycle2 ; loop back
EndLoop2:
popad ; pop registers
ret ; bye
global _start
_start:
nop ; gdb break point
mov eax, -345 ;
call _iprint ;
mov eax, 0x01 ; sys_exit
mov ebx, 0 ; error code
int 0x80 ; край
Because you didn't say about number representation I wrote the following code for unsigned number with any base(of course not too big), so you could use it:
BITS 32
global _start
section .text
_start:
mov eax, 762002099 ; unsigned number to print
mov ebx, 36 ; base to represent the number, do not set it too big
call print
;exit
mov eax, 1
xor ebx, ebx
int 0x80
print:
mov ecx, esp
sub esp, 36 ; reserve space for the number string, for base-2 it takes 33 bytes with new line, aligned by 4 bytes it takes 36 bytes.
mov edi, 1
dec ecx
mov [ecx], byte 10
print_loop:
xor edx, edx
div ebx
cmp dl, 9 ; if reminder>9 go to use_letter
jg use_letter
add dl, '0'
jmp after_use_letter
use_letter:
add dl, 'W' ; letters from 'a' to ... in ascii code
after_use_letter:
dec ecx
inc edi
mov [ecx],dl
test eax, eax
jnz print_loop
; system call to print, ecx is a pointer on the string
mov eax, 4 ; system call number (sys_write)
mov ebx, 1 ; file descriptor (stdout)
mov edx, edi ; length of the string
int 0x80
add esp, 36 ; release space for the number string
ret
It's not optimised for numbers with base of power of two and doesn't use printf from libc.
The function print outputs the number with a new line. The number string is formed on stack. Compile by nasm.
Output:
clockz
https://github.com/tigertv/stackoverflow-answers/tree/master/8194141-how-to-print-a-number-in-assembly-nasm
Related
I'm trying to learn assembly. I wanted to write a simple program that counted to 20 and printed out the numbers. I know you have to subtract ascii '0' from a ascii representation of a number to turn it into it's digit, but my implementation just refuses to work. I still get 123456789:;<=>?#ABCD
Here is my code.
section .bss
num resb 1
section .text
global _start
_start:
mov eax, '1'
mov ebx, 1 ; Filehandler 1 = stdout
mov ecx, 20 ; The number we're counting to
mov edx, 1 ; Size of a number in bytes
l1:
mov [num], eax ; Put eax into the value of num
mov eax, 4 ; Put 4 into eax (write)
push ecx ; Save ecx on the stack
mov ecx, num ; print num
int 0x80 ; Do the print
pop ecx ; Bring ecx back from the stack
mov eax, [num] ; Put the value of num into eax
sub eax, '0' ; Convert to digit
inc eax ; Increment eax
add eax, '0' ; Convert back to ascii
loop l1
mov eax,1 ; System call number (sys_exit)
int 0x80 ; Call kernel
Can anyone see what the problem is? I'm totally hitting a brick wall. I'm using nasm to compile and ld to link.
I am doing a proj. in 64-bit NASM. I have to convert decimal to binary and binary to decimal.
I keep getting segmentation fault after debugging when i call printf.
extern printf
section .bss
decsave: resd 2 ; stores dec->bin conversion
binsave: resd 1
section .data ; preset constants, writeable
dec1: db '1','2','4','.','3','7','5',0
bin1: dq 01010110110101B ; 10101101.10101 note where binary point should be
ten: dq 10
debug: db "debug 124 is %ld", 10, 0
section .text ; instructions, code segment
global main ; for gcc standard linking
main: ; label
push rbp ; save rbp
;parse and convert integer portion of dec->bin
mov rax,0 ; accumulate value here
mov al,[dec1] ; get first ASCII digit
sub al,48 ; convert ASCII digit to binary
mov rbx,0 ; clear register (upper part)
mov bl,[dec1+1] ; get next ASCII digit
sub rbx,48 ; convert ASCII digit to binary
imul rax,10 ; ignore rdx
add rax,rbx ; increment accumulator
mov rbx,0
mov bl,[dec1+2]
sub rbx,48
imul rax,10
add rax,rbx
mov [decsave],rax ; save decimal portion
mov rdi, debug
mov rsi, [decsave]
mov rax,0
call printf
; return using c-style pops to return stack to correct position
; and registers to correct content
pop rbp
mov rax,0
ret ; return
; print the bits in decsave:
section .bss
abits: resb 17 ; 16 characters & zero terminator
section .data
fmts: db "%s",0
section .text
; shift decimal portion into abits as ascii
mov rax,[decsave] ; restore rax to dec. portion
mov rcx,8 ; for printing 1st 8 bits
loop3: mov rdx,0 ; clear rdx ready for a bit
shld rdx,rax,1 ; top bit of rax into rdx
add rdx,48 ; make it ASCII
mov [abits+rcx-1],dl ; store character
ror rax,1 ; next bit into top of rax
loop loop3 ; decrement rcx, jump non zero
mov byte [abits+7],'.' ; end of dec. portion string
mov byte [abits+8],0 ; end of "C" string
push qword abits ; string to print
push qword fmts ; "%s"
call printf
add rsp,8
mov rax,[decsave+16] ; increment to fractional portion
mov rcx,16 ; for printing 3 bits as required in the directions
loop4: mov rdx,0 ; clear rdx ready for a bit
shld rdx,rax,1 ; top bit of rax into rdx
add rdx,48 ; make it ASCII
mov [abits+rcx-1],dl ; store character
ror rax,1 ; next bit into top of rax
loop loop4 ; decrement rcx, jump non zero
mov byte [abits+3],10 ; end of "C" string at 3 places
mov byte [abits+4],0 ; end of "C" string
push qword abits ; string to print
push qword fmts ; "%s"
call printf
add rsp,8
Is there a any other way to get around it?
Thank you.
As Jester pointed out, if the vararg function is not using sse, then al must be zero. There is a bigger issue here:
With the x86-64 calling convention, parameters are not passed on the stack as they are for 32bit, but instead passed through registers. Which registers all depend on what OS your program is written for.
x86 calling conventions
Any good NASM/Intel Assembly programmers out there? If so, I have a question for you!
Every tutorial I can find online, shows the usage of "printf" for printing the actual value of ARGC to the screen (fd:/dev/stdout). Is it not possible to simply print it with sys_write() for example:
SEGMENT .data ; nothing here
SEGMENT .text ; sauce
global _start
_start:
pop ECX ; get ARGC value
mov EAX, 4 ; sys_write()
mov EBX, 1 ; /dev/stdout
mov EDX, 1 ; a single byte
int 0x80
mov EAX, 1 ; sys_exit()
mov EBX, 0 ; return 0
int 0x80
SEGMENT .bss ; nothing here
When I run this, I get no output at all. I have tried copying ESP into EBP and tried using byte[EBP+4], (i was told the brackets de-reference the memory address).
I can confirm that the value when compared to a constant, works. For instance,
this code works:
pop ebp ; put the first argument on the stack
mov ebp, esp ; make a copy
cmp byte[ebp+4],0x5 ; does it equal 5?
je _good ; goto _good, &good, good()
jne _bad ; goto _bad, &bad, bad()
When we "pop" the stack, we technically should get the full number of arguments, no? Oh, btw, I compile with:
nasm -f elf test.asm -o test.o
ld -o test test.o
not sure if that is relevant. Let me know if i need to provide more information, or format my code for readability.
At least 2 problems.
You need to pass a pointer to the thing you want to print.
You probably want to convert to text.
Something like this should work:
SEGMENT .text ; sauce
global _start
_start:
mov ecx, esp ; pointer to ARGC on stack
add byte [esp], '0' ; convert to text assuming single digit
mov EAX, 4 ; sys_write()
mov EBX, 1 ; /dev/stdout
mov EDX, 1 ; a single byte
int 0x80
mov EAX, 1 ; sys_exit()
mov EBX, 0 ; return 0
int 0x80
Everyone's comments where very helpful! I am honored that you all pitched in and helped! I have used #Jester's code,
SEGMENT .text ; sauce
global _start
_start:
mov ecx, esp ; pointer to ARGC on stack
add byte [esp], '0' ; convert to text assuming single digit
mov EAX, 4 ; sys_write()
mov EBX, 1 ; /dev/stdout
mov EDX, 1 ; a single byte
int 0x80
mov EAX, 1 ; sys_exit()
mov EBX, 0 ; return 0
int 0x80
Which works perfectly when compiled, linked and loaded. The sys_write() function requires a pointer, such like in the common "Hello World" example, the symbol "msg" is a pointer as seen in the code below.
SECTION .data ; initialized data
msg: db "Hello World!",0xa
SECTION .text ; workflow
global _start
_start:
mov EAX, 4
mov EBX, 1
mov ECX, msg ; a pointer!
So first, we move the stack pointer into the counter register, ECX, with the code,
mov ecx, esp ; ecx now contains a pointer!
and then convert it to a string by adding a '0' char to the value pointed to by ESP (which is ARGC), by de-referencing it with square brackets, as [ESP] like so,
add byte[esp], '0' ; update the value stored at "esp"
Again, thank you all for the great help! <3
I am a developer who uses high level languages, learning assembly language in my spare time. Please see the NASM program below:
section .data
section .bss
section .text
global main
main:
mov eax,21
mov ebx,9
add eax,ebx
mov ecx,eax
mov eax,4
mov ebx,1
mov edx,4
int 0x80
push ebp
mov ebp,esp
mov esp,ebp
pop ebp
ret
Here are the commands I use:
ian#ubuntu:~/Desktop/NASM/Program4$ nasm -f elf -o asm.o SystemCalls.asm
ian#ubuntu:~/Desktop/NASM/Program4$ gcc -o program asm.o
ian#ubuntu:~/Desktop/NASM/Program4$ ./program
I don't get any errors, however nothing is printed to the terminal. I used the following link to ensure the registers contained the correct values: http://docs.cs.up.ac.za/programming/asm/derick_tut/syscalls.html
You'll have to convert the integer value to a string to be able to print it with sys_write (syscall 4). The conversion could be done like this (untested):
; Converts the integer value in EAX to a string in
; decimal representation.
; Returns a pointer to the resulting string in EAX.
int_to_string:
mov byte [buffer+9],0 ; add a string terminator at the end of the buffer
lea esi,[buffer+9]
mov ebx,10 ; divisor
int_to_string_loop:
xor edx,edx ; clear edx prior to dividing edx:eax by ebx
div ebx ; EAX /= 10
add dl,'0' ; take the remainder of the division and convert it from 0..9 -> '0'..'9'
dec esi ; store it in the buffer
mov [esi],dl
test eax,eax
jnz int_to_string_loop ; repeat until EAX==0
mov eax,esi
ret
buffer: resb 10
programming in assembly requires a knowledge of ASCII codes and a some basic conversion routines. example: hexadecimal to decimal, decimal to hexadecimal are good routines to keep somewhere on some storage.
No registers can be printed as they are, you have to convert (a lot).
To be a bit more helpfull:
ASCII 0 prints nothing but some text editors (kate in kde linux) will show something on screen (a square or ...). In higher level language like C and C++ is it used to indicate NULL pointers and end of strings.
Usefull to calculate string lengths too.
10 is end of line. depending Linux or Windows there will be a carriage return (Linux) too or not (Windows/Dos).
13 is carriage return
1B is the ESC key (Linux users will now more about this)
255 is a hard return, I never knew why it is good for but it must have its purpose.
check http://www.asciitable.com/ for the entire list.
Convert the integer value to a string.
Here i have used macros pack and unpack to convert integers to string and macro unpack to do the vice-versa
%macro write 2
mov eax, 4
mov ebx, 1
mov ecx, %1
mov edx, %2
int 80h
%endmacro
%macro read 2
mov eax,3
mov ebx,0
mov ecx,%1
mov edx,%2
int 80h
%endmacro
%macro pack 3 ; 1-> string ,2->length ,3->variable
mov esi, %1
mov ebx,0
%%l1:
cmp byte [esi], 10
je %%exit
imul ebx,10
movzx edx,byte [esi]
sub edx,'0'
add ebx,edx
inc esi
jmp %%l1
%%exit:
mov [%3],ebx
%endmacro
%macro unpack 3 ; 1-> string ,2->length ,3->variable
mov esi, %1
mov ebx,0
movzx eax, byte[%3]
mov byte[%2],0
cmp eax, 0
jne %%l1
mov byte[%2],1
push eax
jmp %%exit2
%%l1:
mov ecx,10
mov edx,0
div ecx
add edx,'0'
push edx
inc byte[%2]
cmp eax, 0
je %%exit2
jmp %%l1
%%exit2:
movzx ecx,byte[%2]
%%l2:
pop edx
mov [esi],dl
inc esi
loop %%l2
%endmacro
section .data ; data section
msg1: db "First number : " ;
len1: equ $-msg1 ;
msg2: db "Second number : " ;
len2: equ $-msg2 ;
msg3: db "Sum : " ;
len3: equ $-msg3 ;
ln: db 10
lnl: equ $-ln
var1: resb 10
var2: resb 10
str1: resb 10
str2: resb 10
ans: resb 10
ansvar: resb 10
ansl: db ''
l1: db ''
l2: db ''
section.text ;code
global _start
_start:
write msg1,len1
read str1,10
pack str1,l1,var1
write msg2,len2
read str2,10
pack str2,l2,var2
mov al,[var1]
add al,[var2]
mov [ansvar],al
unpack ans,ansl,ansvar
write msg3,len3
write ans,10
write ln,lnl
mov ebx,0 ; exit code, 0=normal
mov eax,1 ; exit command to kernel
int 0x80 ; interrupt 80 hex, call kernel
To assembler, link and run:
nasm -f elf add.asm
ld -s -o add add.o
./add
I'm trying to learn assembly with NASM on 64 bit Linux.
I managed to make a program that reads two numbers and adds them. The first thing I realized was that the program will only work with one-digit numbers (and results):
; Calculator
SECTION .data
msg1 db "Enter the first number: "
msg1len equ $-msg1
msg2 db "Enter the second number: "
msg2len equ $-msg2
msg3 db "The result is: "
msg3len equ $-msg3
SECTION .bss
num1 resb 1
num2 resb 1
result resb 1
SECTION .text
global main
main:
; Ask for the first number
mov EAX,4
mov EBX,1
mov ECX,msg1
mov EDX,msg1len
int 0x80
; Read the first number
mov EAX,3
mov EBX,1
mov ECX,num1
mov EDX,2
int 0x80
; Ask for the second number
mov EAX,4
mov EBX,1
mov ECX,msg2
mov EDX,msg2len
int 0x80
; Read the second number
mov EAX,3
mov EBX,1
mov ECX,num2
mov EDX,2
int 0x80
; Prepare to announce the result
mov EAX,4
mov EBX,1
mov ECX,msg3
mov EDX,msg3len
int 0x80
; Do the sum
; Store read values to EAX and EBX
mov EAX,[num1]
mov EBX,[num2]
; From ASCII to decimal
sub EAX,'0'
sub EBX,'0'
; Add
add EAX,EBX
; Convert back to EAX
add EAX,'0'
; Save the result back to the variable
mov [result],EAX
; Print result
mov EAX,4
mov EBX,1
mov ECX,result
mov EDX,1
int 0x80
As you can see, I reserve one byte for the first number, another for the second, and one more for the result. This isn't very flexible. I would like to make additions with numbers of any size.
How should I approach this?
First of all you are generating a 32-bit program, not a 64-bit program. This is no problem as Linux 64-bit can run 32-bit programs if they are either statically linked (this is the case for you) or the 32-bit shared libraries are installed.
Your program contains a real bug: You are reading and writing the "EAX" register from a 1-byte field in RAM:
mov EAX, [num1]
This will normally work on little-endian computers (x86). However if the byte you want to read is at the end of the last memory page of your program you'll get a bus error.
Even more critical is the write command:
mov [result], EAX
This command will overwrite 3 bytes of memory following the "result" variable. If you extend your program by additional bytes:
num1 resb 1
num2 resb 1
result resb 1
newVariable1 resb 1
You'll overwrite these variables! To correct your program you must use the AL (and BL) register instead of the complete EAX register:
mov AL, [num1]
mov BL, [num2]
...
mov [result], AL
Another finding in your program is: You are reading from file handle #1. This is the standard output. Your program should read from file handle #0 (standard input):
mov EAX, 3 ; read
mov EBX, 0 ; standard input
...
int 0x80
But now the answer to the actual question:
The C library functions (e.g. fgets()) use buffered input. Doing it like this would be a bit to complicated for the beginning so reading one byte at a time could be a possibility.
Thinking the way "how would I solve this problem using a high-level language like C". If you don't use libraries in your assembler program you can only use system calls (section 2 man pages) as functions (e.g. you cannot use "fgets()" but only "read()").
In your case a C program reading a number from standard input could look like this:
int num1;
char c;
...
num1 = 0;
while(1)
{
if(read(0,&c,1)!=1) break;
if(c=='\r' || c=='\n') break;
num1 = 10*num1 + c - '0';
}
Now you may think about the assembler code (I typically use GNU assembler, which has another syntax, so maybe this code contains some bugs):
c resb 1
num1 resb 4
...
; Set "num1" to 0
mov EAX, 0
mov [num1], EAX
; Here our while-loop starts
next_digit:
; Read one character
mov EAX, 3
mov EBX, 0
mov ECX, c
mov EDX, 1
int 0x80
; Check for the end-of-input
cmp EAX, 1
jnz end_of_loop
; This will cause EBX to be 0.
; When modifying the BL register the
; low 8 bits of EBX are modified.
; The high 24 bits remain 0.
; So clearing the EBX register before
; reading an 8-bit number into BL is
; a method for converting an 8-bit
; number to a 32-bit number!
xor EBX, EBX
; Load the character read into BL
; Check for "\r" or "\n" as input
mov BL, [c]
cmp BL, 10
jz end_of_loop
cmp BL, 13
jz end_of_loop
; read "num1" into EAX
mov EAX, [num1]
; Multiply "num1" with 10
mov ECX, 10
mul ECX
; Add one digit
sub EBX, '0'
add EAX, EBX
; write "num1" back
mov [num1], EAX
; Do the while loop again
jmp next_digit
; The end of the loop...
end_of_loop:
; Done
Writing decimal numbers with more digits is more difficult!