Floating-Point
The fraction and exponent can be represented in any form (1's, 2's complement; sign-magnitude)
Consider a numerical example in the decimal (r=10) system:
A = +0.0000068421 ? 10 ^(+3)
we can write this in [fraction, exponent] form as:
A = [+0.0000068421, +3] or [0.6842100000, -2]
Precision is maintained by normalizing a number: shift the fraction (left or right) until the bit to the immediate right of the decimal point is the most significant, non-zero digit. Compute the exponent as appropriate.