### 2-5 Sign
Extension

By "sign extension," we mean to
consider a certain bit position in a word to be the sign bit, and we wish to
propagate that to the left, ignoring any other bits present. The standard way
to do this is with shift left logical followed
by shift right signed. However, if these
instructions are slow or nonexistent on your machine, it may be done with one
of the following, where we illustrate by propagating bit position 7 to the
left:

The "+" above can also be
"-" or "." The second
formula is particularly useful if you know that the unwanted high-order bits
are all 0's, because then the and can be
omitted.