bit shifting arithmetic

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(400*615) >> 4 = 24.6

Except in binary, it doesn't work like this?

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You need to decide. Thinking in base 10, or thinking in base 2. Since you want to do it with simple logic, go with base 2.

Your 'equation' listed above first multiplies by 10^4, then divides by 2^4. That ain't gonna work. Instead of multiplying .0615 by a power of 10, multiply by a power of two (enough to make it an integer), do the math, then shift it back down (divide) by the same power of 2. (or leave it shifted up in preparation for whatever you're going to do next.)

bit shifting is only useful for multiplies when you have only a few 2^n coefficients. for example:

0.75 = 0.5 (2^-1) + 0.25(2^-2)

so 5 x 0.75 = 5x0.5 + 5x0.25

When you have more than a couple, it is more sensible to use a multiplier instead because it can calculate results faster than a large adder chain.

Back to your original example:

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Basically, I don't want to deal with floating points, so I have a problem that was originally

400 * 0.0615 = 24.6

to this

(400*615) >> 4 = 24.6

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Instead of multiplying 0.0615 by 10000, multiply by a power of 2. For example:

= 400 * (0.0615 * 2^16) >> 16

= 400 * 4030 >> 16

= 1612000 >> 16

= 24

If you want to avoid floats and still have fractional values, you will have to use fixed point.