A random access machine is an abstract machine with integer-valued memory registers whose addresses can themselves be computed. An instruction can access a register by its address without traversing all intervening registers (CRC Press LLC 2004).
A word-based variant stores bounded-length sequences of binary digits in its registers. In a logarithmic-word
model for an input of length 
, each memory word has 
binary digits, where
denotes big-O notation. The specified arithmetic
and logical operations on a constant number of words have unit cost (Massachusetts
Institute of Technology 2012, p. 1). An operation on a number spanning several
words must be charged according to the operations it requires. This distinction matters
when specifying the computation time of an algorithm.
