### Integers.

One machine word can contain a SINGLE PRECISION INTEGER in the range . To represent integers outside of this range, so called MULTIPRECISION INTEGER, we use arrays of -bit words. To be precise we consider the -ary (or radix ) expansion of a nonzero integer:

 (33)

where
• every is a digit in the -ary expansion of ,
• determines the sign of ,
• is the number of -digits in the -ary expansion of ,
• .
Then the integer with -digits can be represented by an array (of -bit words) with length since we need
• one word for and
• one word for
The reasonable UNIT OPERATION for integers is the the WORD OPERATION. One can easily check that
• the ADDITION of two integers with at most -digits requires word operations
• the MULTIPLICATION of two integers with at most -digits requires word operations.

Marc Moreno Maza
2008-01-07