We reduce 3-SAT to SUBSET-SUM (with large numbers).
We first assume that every clause in our input formula
has exactly three literals ¨C we can just repeat literals
in the same clause to make this true. Our numbers will be
represented in decimal notation, with a column for each
of the v variables and a column for each clause in the
formula. 

We¡¯ll create an item ai for each of the 2n literals. This
item will have a 1 in the column for its variable, a 1 in
the column of each clause where the literal appears, and
zeroes everywhere else. We also have two items for each
clause, each with a 1 in the column for that clause and
zeroes everywhere else. The target number has a 1 for
each variable column and a 3 for each clause column.
We now have to prove that there is a subset summing to
the target iff the formula is satisfiable. If there is a satisfying
assignment, we choose the item for each literal
in that assignment. This has one 1 in each variable column,
and somewhere from one to three 1¡¯s in each clause
column. Using extra items as needed, we can reach the
target.

Conversely, if we reach the target we must have chosen
one item with a 1 in each variable column, so we have
picked n variables forming an assignment. Since we have
three 1¡¯s in each clause column and at most two came
from the extra items, we must have at least one 1 in each
clause column from our assignment, making it a satisfying
assignment.