Binary combinations

Explanation or usage

With n independent positions and two choices per position, there are 2^n patterns. Three positions yield eight patterns; adding a fourth gives sixteen. Counting patterns does not by itself assign their meanings, and decoding messages of varying lengths requires rules for distinguishing where one message ends and another begins.

Common misunderstandings

Six two-state positions yield only twelve patterns.

In Code

General context reviewed · book attribution and sources pending

In a fixed-length binary-pattern counting exercise, n positions yield 2^n patterns. Whether a blank is included as a pattern depends on the exercise's stated conventions.