There's (almost) always a shorter way ;-)

First, you're doing the if (...) { ... } else { ... } thing a total of 8 times, so you can reduce that portion of your program by a factor of 8 if you do something like this:

use warnings;
use strict;

print "Please input a decimal no. to convert to binary : ";
chomp (my $value = <STDIN>);

apply_mask($value, 128);
apply_mask($value,  64);
apply_mask($value,  32);
apply_mask($value,  16);
apply_mask($value,   8);
apply_mask($value,   4);
apply_mask($value,   2);
apply_mask($value,   1);

sub apply_mask {
    my $value = shift;
    my $mask  = shift;
    if ($value & $mask) {
        print "1";
    } else {
        print "0";
    }
}
[download]

But since the numbers 1 ... 128 are easily computable as powers of two, you could simplify it to:

use warnings;
use strict;

print "Please input a decimal no. to convert to binary : ";
chomp (my $value = <STDIN>);

foreach my $power (0..7) {
    # Originally 2 ** $power, but that's backwards!
    my $mask = 2 ** (7 - $power);
    apply_mask($value, $mask);
}


sub apply_mask {
    my $value = shift;
    my $mask  = shift;
    if ($value & $mask) {
        print "1";
    } else {
        print "0";
    }
}
[download]

By the way, just to show you that TMTOWTDI (= "There's more than one way to do it!" = the Perl motto), here's a lookup table solution which trades memory for speed (ie. uses a lot of memory, but is relatively fast):

use strict;
use warnings;

my @binary_table = qw(
        0        1       10       11      100      101      110      1
+11
     1000     1001     1010     1011     1100     1101     1110     11
+11
    10000    10001    10010    10011    10100    10101    10110    101
+11
    11000    11001    11010    11011    11100    11101    11110    111
+11
   100000   100001   100010   100011   100100   100101   100110   1001
+11
   101000   101001   101010   101011   101100   101101   101110   1011
+11
   110000   110001   110010   110011   110100   110101   110110   1101
+11
   111000   111001   111010   111011   111100   111101   111110   1111
+11
  1000000  1000001  1000010  1000011  1000100  1000101  1000110  10001
+11
  1001000  1001001  1001010  1001011  1001100  1001101  1001110  10011
+11
  1010000  1010001  1010010  1010011  1010100  1010101  1010110  10101
+11
  1011000  1011001  1011010  1011011  1011100  1011101  1011110  10111
+11
  1100000  1100001  1100010  1100011  1100100  1100101  1100110  11001
+11
  1101000  1101001  1101010  1101011  1101100  1101101  1101110  11011
+11
  1110000  1110001  1110010  1110011  1110100  1110101  1110110  11101
+11
  1111000  1111001  1111010  1111011  1111100  1111101  1111110  11111
+11
 10000000 10000001 10000010 10000011 10000100 10000101 10000110 100001
+11
 10001000 10001001 10001010 10001011 10001100 10001101 10001110 100011
+11
 10010000 10010001 10010010 10010011 10010100 10010101 10010110 100101
+11
 10011000 10011001 10011010 10011011 10011100 10011101 10011110 100111
+11
 10100000 10100001 10100010 10100011 10100100 10100101 10100110 101001
+11
 10101000 10101001 10101010 10101011 10101100 10101101 10101110 101011
+11
 10110000 10110001 10110010 10110011 10110100 10110101 10110110 101101
+11
 10111000 10111001 10111010 10111011 10111100 10111101 10111110 101111
+11
 11000000 11000001 11000010 11000011 11000100 11000101 11000110 110001
+11
 11001000 11001001 11001010 11001011 11001100 11001101 11001110 110011
+11
 11010000 11010001 11010010 11010011 11010100 11010101 11010110 110101
+11
 11011000 11011001 11011010 11011011 11011100 11011101 11011110 110111
+11
 11100000 11100001 11100010 11100011 11100100 11100101 11100110 111001
+11
 11101000 11101001 11101010 11101011 11101100 11101101 11101110 111011
+11
 11110000 11110001 11110010 11110011 11110100 11110101 11110110 111101
+11
 11111000 11111001 11111010 11111011 11111100 11111101 11111110 111111
+11
);

print "Please input a decimal no. to convert to binary : ";
chomp (my $value = <STDIN>);
my $binary = $binary_table[$value];
if (!defined($binary)) {
    die "Sorry, value $value isn't in the table!\n";
}
print "Decimal $value = Binary $binary\n";
[download]

It only works for values from 0 to 255, though.

Update:  Oh, yes ... if you want shorter code instead of faster execution, here's a fancier way of writing it fairly succinctly:

use warnings;
use strict;

print "Please input a decimal no. to convert to binary : ";
chomp (my $value = <STDIN>);
print map { ($value & (1 << (7 - $_)))? 1: 0 } ( 0 .. 7 );
print "\n";
[download]

Update 2:  Reversed the effective order the bits are printed in to make it msb first and lsb last (thanks for pointing that out ysth++).