R, 87 88 bytes
Wall blocks represented by an 8, because, well lots of eights.
write(ifelse((I=sapply(scan(),intToBits))[(M=max(which(I>0,T)[,1])):1,],8,' '),1,M,,'')
Input integer list is converted to array of bits which are trimmed of trailing 0 bits and reversed.
The reduced array is then output using write and a column width which was determined when the array was trimmed.
ifelse() is the only IF option that works on vectors unfortunately.