2 Sep
2006
2 Sep
'06
11:01 a.m.
On Fri, 1 Sep 2006 23:45:47 -0400 (EDT), der Mouse
<mouse at Rodents.Montreal.QC.CA> wrote:
In the embedded world, the use of fixed point arithmetic is rampant.
If you use a fixed point DSP, the use of pointed hexadecimal makes
life infinitely easier than having to continually convert between
decimal and hex. The issues of underflow/overflow are immediately
obvious. The last time I checked, those little buggers outnumber the
number of IEEE floating-point PCs of all flavors ever made.
> I have
never seen a hex number with a decimal point anyway...
Nor will you; as Fred already pointed out, it's a hexadecimal point.
That aside, they do exist, though they're rare. While practically
everything these days uses IEEE floating-point, which is binary-based,
there have been machines with floating-point arithmetic that worked in
other bases, like octal or hex. For them, speaking of the "decimal"
point in a number printed in hex notation makes perfect sense. > As quick exercises, 1) what is the binary fraction
for PI?
By way of trusty Mathematica: Pi to 1000 decimal places converted to
base 2:
In[1]:=
BaseForm[N[Pi,1000],2]
Out[1]//BaseForm=
"
11.001001000011111101101010100010001000010110100011000010001101001100010
01\
100011001100010100010111000000011011100000111001101000100101001000000100
100111\
000001000100010100110011111001100011101000000001000001011101111101010011
000111\
011000100111001101100100010010100010100101000001000011110011000111000110
100000\
001001101110111101111100101010001100110110011110011010011101001000011000
110110\
011000000101011000010100110110111110010010111110001010000110111010011111
110000\
100110101011011010110110101010001110000100100010111100100100001011011010
101110\
110011000100101111001111110110001101111010001001100010000101110100110100
110001\
101111110110101101011000010111111111101011100101101101111010000000110101
101111\
110110111101110001110000110101111111011010110101000100110011111101001011
010111\
010011111001001000001000101111100010010110001111111100110010010010010100
001100\
110010100011110110011100100010110110011110111000010000000000111110010111
000101\
000010110001110111111000001011001100011011010010010000011011000011100010
101011\
101001110011010011010010001011000111111101010001111110100100100110011110
101111\
110000011011001010101110100100011110111001010001110101101100101100001110
001100\
010111100110101011000100000100001010101001010111011100111101101010100101
001000\
001110111000010010110100101100110110101100111000011000011010101001110010
010101\
011110010011000000001001111000101110100011011000000100011001010000110000
010000\
101111100001100101001000001011110010001100010111000110110110011100011101
111100\
011100111100111011100101100000110000000111010000110000000111001101100100
111100\
000111010001011101100000001111010001010001111101101011100010101011101111
100000\
110111101001100010100101100100111011110001010111100101111110110100101010
101100\
000010111000110000011100110010101010010010111110011101010100101010110101
011100\
101000101011101001000100110000110001001100011111010000001010001000000010
101011\
100101000111001011010100010101010101011000100001011011010110100110011000
101110\
000110100000100010100000111101000110011101010000101010100100001101010111
101111\
100011100101110100110010011101100111110111000010100000100010110001101101
111101\
111000010101000101011101010011100010101011101011101000001100000110001111
101101\
100111001011100001111100001011010011011100001111001001100011110101011111
101011\
010111010001100110110110000100100110011110101110001111010001100100101001
110000\
001001010001001010110000110011101110011101110001111010010001001100001101
011010\
010111011100110101111110001001011111111101000000110110110011000101000001
000011\
001001101100001110110000000100111001100111110110010000110101001100100010
100100\
001111100101011000110000001011101111011001000000000110010111011111000010
001011\
101010111011110100110000101011101011011000111011100001001100010001100000
010111\
010110110010100011011100010000010001110001001001111101000000111010011100
101101\
010110011000101000011110110110101101111111100111000001111110100010000100
011100\
100101110000010110100010010000010101001001000010000100000000001000110100
111001\
000111100000100101010011110000111111001101101011110001000011100011001101
000010\
000101111011011101001011011001001101001100111000011001001110001100001101
010111\
101001110001000111100000110101001010001101000001101001011011000010101000
010111\
101101000100101100000111110100111001010001010101101010001001100111010001
101101\
110111011110000101101101100000100110111101000111100"\_2\)
CRC