Quick Question

How do you convert 6.7 to binary. 6 is just 110. But how do you convert something that is less than 1.

Thanks

Hello Saturn;
Easy.
6.7 converts to 01000000110101100110011001100110
No, really. I mean it.
IEEE has developed a binary representation for floating-point values in single-precision (32 bit REAL) or double-precision (64-bit REAL) formats that is followed by most (if not all) computer and PLC systems. It is designated IEEE754.
This first link takes you to a binary converter for floating-point values; the second shows you a bit of the math theory behind this representation.

http://www.h-schmidt.net/FloatConverter/IEEE754.html
https://en.wikipedia.org/wiki/Single-precision_floating-point_format

Hope this helps,
Daniel Chartier

Normally, you either use a FLOAT instead of an INT, or you multiply the INT by a factor of 10, so its a whole number. 6.7 becomes 67, and you have to treat it special in your code.

I've never come across a standard for how a non-integer binary would be written (besides as a float), but here is my thought:

If normal binary is the power of 2 increasing as you go right (2^0=1, 2^1=2, 2^2=4, etc) , I would think that you could also extend the binary to the left by decreasing (2^-1=.5, 2^-2=.25, etc). This is how normal decimal notation works. The trick is that the fraction part is an approximation. 6.7 really means "some number between 6.65 and 6.74" (or something similar, depending how you round). So just as you represent the 6 as 4*1+2*1+1*0, you could represent .7 as .5*1+.25*0+.125*1+.0625*1=.6875.

Thus 6.7 gets rounded to 6.6875 and becomes 110.1011.

The actual .7 part would be very hard to represent in terms of powers of 2. It becomes an infinite series, getting ever closer, but never exactly there.