Now take that extend it to the binary digital representation.Quote:
Originally Posted by MrPrena
2/3 = 1/2 + 1/8 + 1/32 + 1/128 + 1/512 + ...
= 0.1010101 ...
In actual single precision floating point, the 32 bits of a computer word are split using the first bit for the sign (positive or negative), 8 bits for the exponent, and 23 bits for the mantissa.
You can see how this works at https://www.exploringbinary.com/floa...int-converter/ . Enter a decimal number, specify output in binary and click convert. Now for some real fun, specify decimal output as well and you can see what that binary representation really translates to. In the case of 2/3 at double precision, it's 0.666666666666666662965923241249478198587494439697 2656 .... that's generally "good enough for government work" but the errors pile up with each multiplication or division. A mechanical or electronical engineer (much less a general contractor) should never have to worry about that. Someone calculating the gravity boosts for an interplanetary probe using a radioactive thermal generator that needs to swing by the Earth a couple of times at altitudes of 1/20-1/10 the radius of the Earth does ...
