I have the following number in binary:
$$ 0.111_2 = 0 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} $$
I need to find the number such that it's bigger than the current and there is no number in between represented within the given number of places after the radix point (no numbers like 0.1111 - 4 places after the radix point). How can I do that?
I can make parallel with decimal system, where for the number 0.3 the least bigger number is 0.4, and no other number that have 1 place after the radix exist between 0.3 and 0.4
Add $1$ in the last place. In your case, add $\frac{1}{8}$ to get the number $1$, which we should write as $(1.00)_2$ to keep the number of significant figures at $3$.
EDIT: Adding anything smaller than $1$ in the last place would automatically increase the number of significant figures in the result. Specifially, if we start with $(1.11)_2 \times 2^{-1} = (0.111)_2$ and add $\frac{1}{32} = (0.00001)_2$ we obtain the result $(0.11101)_2 = (1.1101)_2 \times 2^{-1}$ which has $5$ significant figures.