More About Patterns

Number of Bits	Number of Patterns	Number of Patterns as power of two
1	2	21
2	4	22
3	8	23
4	16	24
5	32	25
6	64	26
7	128	27
8	256	28
9	512	29
10	1024	210

Many calculations involving bit patterns use the following familiar fact of arithmetic. (Although the fact is familiar, confusion is even more familiar. Be sure you know this factoid.)

2^(N+M)   =   2^N × 2^M

It is not too much work to extend the table, as shown at right. You can always make this table from scratch, but memorizing a few key values does not hurt.

The numbers of patterns that can be formed with 10 or more bits are usually expressed in terms of kilobytes (= 2¹⁰) or megabytes (= 2²⁰). For example, how many patterns can be formed from 24 bits?

2²⁴   =   2⁴ × 2²⁰   =   16 Meg

The power of two (24) splits into a small part (2⁴) and a part that has a name (2²⁰ = Meg). This is a useful trick you can use to amaze your friends and impress employers.

Some audio cards use 12 bits to represent the sound level at an instant in time (12 bits per sample). How many signal levels are represented?

2¹² = 2² × 2¹⁰ = 4K levels