G'day gblack,

Welcome to the Monastery.

Here's one way to do this using Math::BigInt::GMP.

#!/usr/bin/env perl

use 5.010;
use strict;
use warnings;

use Math::BigInt lib => 'GMP';

for my $number (57, '886545601050728061451195', '0x' . 'b' x 20) {
    say "Number: $number"; 
    say "Array:  @{get_array($number)}";
    say 'Bits:   ', scalar @{get_array($number)};

    for (0 .. 5) {
        say "Bit $_:  ", is_bit_set($number, $_);
    }
}

{
    my %cache;

    sub get_array {
        $cache{$_[0]} // gen_array($_[0])
    }

    sub is_bit_set {
        ($cache{$_[0]} // gen_array($_[0]))->[$_[1]]
    }

    sub gen_array {
        $cache{$_[0]} = [
            reverse split //, substr Math::BigInt::->new($_[0])->as_bi
+n(), 2
        ]
    }
}
[download]

I tested with your example number (57) and an 80-bit number in stringified, decimal (886545601050728061451195) and hexidecimal (0xbbbbbbbbbbbbbbbbbbbb) representations:

Number: 57
Array:  1 0 0 1 1 1
Bits:   6
Bit 0:  1
Bit 1:  0
Bit 2:  0
Bit 3:  1
Bit 4:  1
Bit 5:  1
Number: 886545601050728061451195
Array:  1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 
+1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1
+ 0 1 1 1 0 1 1 1 0 1 1 1 0 1
Bits:   80
Bit 0:  1
Bit 1:  1
Bit 2:  0
Bit 3:  1
Bit 4:  1
Bit 5:  1
Number: 0xbbbbbbbbbbbbbbbbbbbb
Array:  1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 
+1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1
+ 0 1 1 1 0 1 1 1 0 1 1 1 0 1
Bits:   80
Bit 0:  1
Bit 1:  1
Bit 2:  0
Bit 3:  1
Bit 4:  1
Bit 5:  1
[download]

If you're not going to be doing multiple operations on the same number, you might be better off without the cache.

I see others have suggested solutions. I'd tailor these to your specific requirements and then Benchmark.

---

---

Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!

Titles consisting of a single word are discouraged, and in most cases are disallowed outright.

Read Where should I post X? if you're not absolutely sure you're posting in the right place.

Please read these before you post! —

• How do I compose an effective node title?
• How do I post a question effectively?
• Markup in the Monastery

Posts may use any of the Perl Monks Approved HTML tags:

a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr

You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)

	For:		Use:
	&		&
	<		&lt;
	>		&gt;
	[		&#91;
	]		&#93;

Link using PerlMonks shortcuts! What shortcuts can I use for linking?

See Writeup Formatting Tips and other pages linked from there for more info.