Abstract
For each function on bit strings, its restriction to bit strings of
any given length can be computed by a finite instruction sequence that
contains only instructions to set and get the content of Boolean
registers, forward jump instructions, and a termination instruction.
Backward jump instructions are not necessary for this, but instruction
sequences can be significantly shorter with them. We take the function
on bit strings that models the multiplication of natural numbers on
their representation in the binary number system to demonstrate this
by means of a concrete example. The example is reason to discuss
points concerning the halting problem and the concept of an algorithm.