Let b$31,$ b$30,$ b$29,...$ b$1,$ b$0$ correspond to the $32$ bits within a CPU register. The unsigned integer represented by this $32-$bit pattern corresponds to the following polynomial in powers of two:

P$\_$unsigned $=$ b$31*(2^31)+$ b$30*(2^30)+$ b$29*(2^29)+...+$ b$1*(2^1)+$ b$0*(2^0)$

where, of course, each bn is either $0$ or $1$

The two$$s complement signed integer represented by the $32-$bit pattern corresponds to the following polynomial in powers of two where the leftmost bit $($b$31)$ is multiplied by $(2^31)$:

P$\_$signed $=$ b$31*[-(2^31)]+$ b$30*(2^30)+$ b$29*(2^29)+...+$ b$1*(2^1)+$ b$0*(2^0)$