store them in a scalar in binary. e.g. "0755"
I just want to store those 4 numbers in a scalar.

sprintf returns a string, and the "4 numbers" includes a leading zero which is just decoration indicating that the number is octal (base 8). Converting that string into a numeric will only remove the leading zero. If you want the value as an integer (which I assume is what you mean by 'binary') then ignore the printf or sprintf:

use warnings;
use strict;
use Devel::Peek;

my $file = $0;

my $mode = sprintf '%04o', (stat $file)[2] & 07777;
print "sprintf Permissions are $mode\n";
print "\twhich is ",oct($mode)," in decimal\n";
print Dump(\$mode),"\n\n";

my $n_mode = (stat $file)[2] & 07777;
print "stat Permissions are $n_mode decimal\n";
print Dump(\$n_mode),"\n";
[download]

In the output the string scalar $mode is "0666" but the integer scalar "$n_mode is 438:

sprintf Permissions are 0666
        which is 438 in decimal
SV = RV(0x3a1b8) at 0x3a1ac
  REFCNT = 1
  FLAGS = (TEMP,ROK)
  RV = 0x18abfd4
  SV = PV(0x3807c) at 0x18abfd4
    REFCNT = 2
    FLAGS = (PADMY,POK,pPOK)
    PV = 0x18b1614 "0666"\0
    CUR = 4
    LEN = 8


stat Permissions are 438 decimal
SV = RV(0x3a1b8) at 0x3a1ac
  REFCNT = 1
  FLAGS = (TEMP,ROK)
  RV = 0x18bada4
  SV = PVIV(0x18a0f4c) at 0x18bada4
    REFCNT = 2
    FLAGS = (PADMY,IOK,POK,pIOK,pPOK)
    IV = 438
    PV = 0x18a1f2c "438"\0
    CUR = 3
    LEN = 4
[download]

You can see that $mode does not have an integer value (IV) at that point, only a string value (PV).