Multiplying intervals in Two's complement
If $0 \leq a,b,c,d$ then $[a,b] [c,d] = [ac,bd]$. The trouble begins when numbers can be negative. If $a,b&lt;0$ then $[a,0][b,0]=[0,ab]$. If $a&lt;0&lt;b$ then $[a,0][0,b] = [ab,0]$. And so on. To consider intervals straddling $0$, partition them into their positive and negative parts.

Summarizing, I wouldn't say that it is "impossible" to find an algorithm for multiplying intervals, only that you have to consider numerous cases. Good luck.