Here's another approach, based on my guess that you're processing 'text' strings (of any length: 16 hex bytes used for example) consisting of any combination of hex digits and whitespace. (Assumes: '01' == 0b00000001 and '0304' == 0b0000001100000100 and etc.)

>perl -wMstrict -le
"my $str = qq{ 01 02 03 \n 04 00 E0 0a 00 00 00 00 00 00 00 00 00 \n};
 (my $bits = $str) =~ s{[^[:xdigit:]]}{}xmsg;
 $bits = unpack 'B*', pack 'H*', $bits;
 my @ones_offsets;
 push @ones_offsets, $-[1] while $bits =~ m{(1)}xmsg;
 print qq{'$str'};
 print qq{'$bits'};
 print qq{no one bits found} unless @ones_offsets;
 print qq{1 bit at offset $_} for @ones_offsets;
"
' 01 02 03
 04 00 E0 0a 00 00 00 00 00 00 00 00 00
'
'000000010000001000000011000001000000000011100000000010100000000000000
+00000000000000000000000000000000000000000000000000000000000'
1 bit at offset 7
1 bit at offset 14
1 bit at offset 22
1 bit at offset 23
1 bit at offset 29
1 bit at offset 40
1 bit at offset 41
1 bit at offset 42
1 bit at offset 52
1 bit at offset 54
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If BrowserUk's guess is right and you already have the data as raw binary string (say, in $bits), just drop the
    $bits = unpack 'B*', pack 'H*', $bits;
statement and all before it, and change that statement to
    $bits = unpack 'B*', $bits;
instead (tested).