32nd format (thirty seconds)
In working with trading systems, I came across an unusual format for representing numbers representing securities quotes, in particular for US government bonds. For example, the price presented
The trick here is that this is not a familiar decimal notation. For example,
So, this format for writing fractional numbers is called "thirty seconds" or
where
or
that is, for the number
In order for the formula to be correct, it
It can be seen that in three fractional digits, not 1000 parts are encoded, as in the decimal system, but only 256 (32 * 8).
So again: if it is written
The reverse translation formula from decimal to format is
If
The component
No matter how bizarre this method of recording cash amounts looks, it is traders who use it (not to be confused with raiders), for example, when trading in US government bonds. I can assume that this is just a legacy of the times when not everyone knew fractional decimal numbers, and writing parts of the whole in the form of natural fractions is much closer to human nature. Divide the pile into two, three, etc. parts can even be a child untrained in decimal fractions.
The format is strange, but you have to know it.
100-31
does not mean 100 dollars and 31 cents, or 100-127
does not make much sense at all, since there is only 100 cents in one dollar, not 1000, and there is no need to reserve three decimal places for the fractional part.The trick here is that this is not a familiar decimal notation. For example,
100-31
in decimal it is equal to 100.97265625
, but 100-127
matches 100.40234375
. So, this format for writing fractional numbers is called "thirty seconds" or
32nd
. For visual convenience and a clear difference from the decimal form, a small dash is used as a separator instead of a dot. But the number itself in general has the following format: AAA.XXY
where
AAA
is the integer part of the number that has the same meaning as in the decimal system. XX
- this is the number of 1/32
shares from the fractional part, and Y
is the number of eights ( 1/8
) in the last 1/32
fraction. Despite the vague description, the transfer formula for the number AAA.XXY
format 32nd
to decimal format is quite simple:D = AAA + (XX + Y * 1/8) * 1/32
or
D = AAA + XX * (1/32) + Y * (1/256)
that is, for the number
100-127
AAA = 100, XX = 12, Y = 7, therefore: D = 100 + 12/32 + 7/256 = 100.40234375
In order for the formula to be correct, it
XX
can take values only from "00"
to "31"
, and Y
from "0"
to "7"
. Also, when writing, the Y
number 4
can be replaced by +
, and "0"
by a space. That is, 100-31
in full form, it is equal 100-310
, but 100-12+
equivalent 100-124
. It can be seen that in three fractional digits, not 1000 parts are encoded, as in the decimal system, but only 256 (32 * 8).
So again: if it is written
100-12+
, then it is 100.39062500
in decimal system. The reverse translation formula from decimal to format is
32nd
not much more complicated. Let beD
decimal:: A = TRUNC(D)
XX = TRUNC((D - A) * 32)
Y = ((D - A) * 32 - XX) * 8
TRUNC
is the function of taking the integer part. If
Y
equal to 0, then you can not write this digit, and if 4, then you can replace it with +
. The component
Y
must be integer. Otherwise, the presence of the fractional part of y Y
is a sign that the original decimal number D
does not have a format mapping 32nd
(only 256 values of the fractional part out of all 1000 possible can have a correspondence in the format 32nd
).No matter how bizarre this method of recording cash amounts looks, it is traders who use it (not to be confused with raiders), for example, when trading in US government bonds. I can assume that this is just a legacy of the times when not everyone knew fractional decimal numbers, and writing parts of the whole in the form of natural fractions is much closer to human nature. Divide the pile into two, three, etc. parts can even be a child untrained in decimal fractions.
The format is strange, but you have to know it.