Binary scaling: Difference between revisions

Revision as of 22:57, 5 February 2018

Revision as of 11:11, 21 February 2018

Line 9:

Binary points obey the mathematical laws of [[exponentiation]].

To give an example, a common way to use [[Arbitrary-precision arithmetic|integer arithmetic]] to simulate floating point, using 32 bit numbers, is to multiply the coefficients by 65536.

Using [[binary scientific notation]], this will place the binary point at 1B16B16.

For instance, to represent 1.2 and 5.6 floating point real numbers as 1B16B16 one multiplies them by 2¹⁶, giving 78643 and 367001.

Multiplying these together gives

Line 19:

28862059643

To convert it back to 1B16B16, divide it by 2¹⁶.

This gives 440400B16, which when converted back to a floating point number (by dividing again by 2¹⁶, but holding the result as floating point) gives 6.71999.