It becomes a slightly physical talk, writing zero means changing one certain point into the state of zero (off) magnetically.
In spite of the work trying to changing the state, previous state is faintly left magnetically. So someone could read the information from the faint remnant magnetization( I do not know how to do it.).
The basic idea of erasing disks is that nobody can guess the original value by writing in various patterns repeatedly.  Although it takes times.

Bellow are major standards of erasing disks.

• US Secretary of Defense. DoD5220.22-M.   a character -> its complement -> random -> verify

• US Army. AR380-19. random -> a character -> its complement

• US Navy. NAVSO P-5239-26.

ff(hex) -> 001001.... 11(32bit bin) -> random -> verify

• US Air Force.  00(hex) -> ff(hex) -> a character -> varify(10%)

• Gutmann's way.  35 times writing

DoD5220.22-M 
Supplement 1 
Feb-95

Overwrite all locations with a character, its complement, then with a random
character. 
Verify that all sectors have been overwritten and that no new bad sectors have
occurred. 

---------------------------------------------
• US Army
http://www.fas.org/irp/doddir/army/

AR380-19
Information Systems Security
27 February 1998

Overwrite all locations three times (first with random charactor, second time with a
specified charactor,third time with the compliment of the specified charactor).

---------------------------------------------
• US navy
http://www.fas.org/irp/doddir/navy/

NAVSO P-5239-26
Remanence Security Guidebook
SEPTEMBER 1993

(1) The preferred method for disk data storage media that may be purged by overwriting is to:
(a) Write all 1's to every block.
(b) MFM: Write a "1" in low order bit; a "0" in the next most significant bit; and "1"s in the remaining bits comprising the data block. RLL: Write "0010011111..1111" (least significant bit ... most significant bit) for 32 bits and repeat this pattern throughout the data block. Repeat the appropriate pattern for all addressable data blocks.
(c) Write a nonlinear pseudorandom bit sequence to all locations. This sequence is not predictable without knowledge of the generating algorithm. One such sequence is the output of an encrypting algorithm (e.g., Data Encryption Standard). In this application a biased algorithm (i.e., producing more zeros than ones (or vice versa)) is acceptable. The sequence should not repeat at the same offset on any two blocks on the disk drive. A different starting point for the pseudorandom bit sequence should be used for each disk drive.
(d) Verify the overwrite by reading the last data written to the data storage media. You should read nothing but the pseudorandom sequence.

(2) An alternate method when the required data patterns cannot be generated is to use the following simpler but less effective technique:
(a) Write a single character (e.g: hex EB) to all addressable locations.
(b) Write the previous character's compliment (i.e., hex 14) to all addressable locations.
(c) Write a random character (e.g., hex 5C) to all addressable locations.
(d) Verify the overwrite by reading the last data written to the data storage media. You should read nothing but the random character.

---------------------------------------------
• US AirForce
http://cryptome.org/afssi5020.htm

AIR FORCE SYSTEM SECURITY INSTRUCTION 5020
REMANENCE SECURITY

20 August 1996

3.3.1. Clearing. Functioning sealed drives and Bernoulli cartridges may be cleared by overwriting all addressable locations with binary zeros (i.e., 0000 0000) then binary ones (i.e., 1111 1111). Then, overwrite all addressable locations with any character (i.e., "a"). Verify the overwrite procedure by randomly re-reading (recommend 10%) the overwritten information to confirm that only the overwrite character can be recovered. This media may also be cleared using a Type I1 degausser.

---------------------------------------------
• Gutmann's way
http://www.cs.auckland.ac.nz/~pgut001/pubs/secure_del.html
Secure Deletion of Data from Magnetic and Solid-State Memory

35 times.