There're 32 bits not 31. To be presize, the max value stored in 32 bits is 2^32-1. See UINT_MAX at http://msdn.microsoft.com/library/default.asp?url=/library/en-us/vccelng/htm/class_34.asp.

>
>2^0=1
>2^1=2
>2^2=4
>2^3=8
>2^4=16
>2^5=32
>2^6=64
>2^7=128
>2^8=256
>2^9=512
>2^10=1024
>2^11=2048
>2^12=4096
>2^13=8192
>2^14=16384
>2^15=32768
>2^16=65536
>2^17=131072
>2^18=262144
>2^19=524288
>2^20=1048576
>2^21=2097152
>2^22=4194304
>2^23=8388608
>2^24=16777216
>2^25=33554432
>2^26=67108864
>2^27=134217728
>2^28=268435456
>2^29=536870912
>2^30=1073741824
>2^31=2147483648
>__________
>3,221,225,472 (Total of all 1's)
>