That's because the packing process has caused the IV (integer variable) that held the 0 value to be converted to a PV (string variable) which carries extra, behind-the-scenes overhead:

[0] Perl> $a = 0; print size $a;;
24
[0] Perl> $b = pack 'b*', 0; print size $b;;
56
[0] Perl> print Dump $a;;
SV = IV(0x3e74270) at 0x3e74278
  REFCNT = 1
  FLAGS = (IOK,pIOK)
  IV = 0

[0] Perl> print Dump $b;;
SV = PV(0x11c110) at 0x3e6c6d8
  REFCNT = 1
  FLAGS = (POK,pPOK)
  PV = 0x3ecd828 "\0"\0
  CUR = 1
  LEN = 8

[download]

As you can see, the PV (string) has a couple of extra internal control fields (CUR & LEN) plus a pointer that points to the actual string which itself consists of one 0 byte to hold the (single) bit -- you cannot pack less that 8 bits; its teh way computers work! -- and a second 0 byte which is to ensure that the string is "null terminated" -- as all strings must be for many C language library routines to work; internally Perl uses the C runtime library.

But, you are being deceived by the simplicity of your test. Let's try something a little more representative of your application:

[0] Perl> $x = join '', map{ rand() < 0.5 ? 0 : 1 } 1 .. 880;;
[0] Perl> print size $x;;
936
[0] Perl> print Dump $x;;
SV = PV(0x3e964e0) at 0x337708
  REFCNT = 1
  FLAGS = (POK,pPOK)
  PV = 0x3e8d8c8 "0011011011100111000000101011100011111101100011111101
+101111001100000111111011010111101100110101101001011000010100111001110
+110000000100010001111011100010111111111010101001010011110111100110001
+111100100110000101100001001011100110100011000011011001100101110111100
+000010100011110010101111110101011111100100100000111110110001101111110
+111000100000111010101000010001000001110100111110010100100101011011100
+1010110000110001001011101010010000010001011011
  CUR = 880
  LEN = 888

[0] Perl> $y = pack 'b*', $x;;
[0] Perl> print size $y;;
160
[0] Perl> print Dump $y;;
SV = PV(0x3e967b0) at 0x3e6c3f0
  REFCNT = 1
  FLAGS = (POK,pPOK)
  PV = 0x3dff038 "l\347@\35\277\361\3333\370\2557ki(\347\6D\274\243\37
+7*\345=\343\223\241!\235\305\260\231\356\201\342\251_\375$\370\306~Gp
+\25\"\270|Jj\247\206\221\256\4\321\16\262?\334\355\22\304S\370nh\325%
+\232K\376\235\34\35L\377\330\4a6\314_\314\222\336\373\375\371m[\246\2
+46g\326e\37\36\23j5\2\346\324O\v|\272s\236\3"\0
  CUR = 110
  LEN = 112

[download]

And there you have it. The fixed internal overhead hasn't changed, but the length of the string (CUR) has reduced from 880 to 110; and teh actual memory use has reduced from 936 bytes to 160 bytes.

And if that all still doesn't make any sense to you; download and spend a week reading this and then come back with any remaining questions.

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

In reply to Re^5: Bit handling in Perl by BrowserUk
in thread Bit handling in Perl by Anonymous Monk

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