Weekly Classic Computer Trivia Question (20141205)

[Peter Corlett]

On Fri, Dec 05, 2014 at 06:05:20PM -0500, Jerome H. Fine wrote:
[...]
> Assuming that 1 terabyte is 2 ** 40 bytes [...]

It's not, it's 10**12.  Every other use of SI multipliers are powers-of-ten,
and computers are not special little snowflakes entitled to be different.

As it happens, a disk with a nominal capacity of 1TB will actually contain
exactly 1,000,204,886,016 bytes[0], which is a quite curious number.  Unless
I've screwed up my maths, the capacity of a drive with a nominal capacity of X
TB is exactly 1,000,194,048,000X + 10,838,016 bytes.

Those numbers factorise to 2**17 * 3**3 * 5**3 * 7*17 * 19 and 2**13 * 3**3 *
7**2 respectively.  Now they're going to be divisible by 2**12 as that's the
sector size, but the remaining factors do not suggest any obvious rounding-off
boundary.


[0] The data sheet I have for Seagate's 1TB ST1000DM003 gives its capacity as
    1,953,525,168 (512-byte) sectors, with the other disks sharing the data
    sheet also having sector counts ending in 168.  WD's data sheet for the 1TB
    WD10EZEX claims 1,953,525,169 sectors, but the other disks on that data
    sheet have sector counts ending 168 and 448.  I thus believe the 169 to be
    a typo of 168, as it would mean that the disk's capacity is not a multiple
    of the 4096-byte sector size typical of large disks.

    It is increasingly-rare to find exact capacities on data sheets, so I have
    not checked against other manufacturers, but I gather that they have all
    agreed to give their disks the same geometry for a given nominal advertised
    capacity.