Formula for how many combinations possible with 1 and 0 pattern and what branch

Question

How would one write the formula to calculate all possible combinations from a pattern with $4$ integers that are either $1$ or $0$.

Example of some possible patterns:

$0001, ~1010, ~0000, ~1111$

At first I was thinking $4 \cdot 4 \cdot 4 \cdot 4$ or $ 4^4 = 256.$ But I am not sure how to check.

Also what branch of mathematics would this fall under? (Example: Arithmetic, Algebra, etc.)

As an aside, the numbers can be interpreted as base2 numbers... the numbers being $0000,0001,0010,0011,0100,0101,\dots,1110,1111$, or when interpreted away from binary into decimal as the numbers $0,1,2,3,4,5,\dots,15$ — JMoravitz, Mar 06 '20 at 15:15

score 2 · Accepted Answer · edited Mar 06 '20 at 15:21

2

At each position, you have $2$ options, hence in total, we have $2^4$ patterns.

Relevant topic: Combinatorics.

edited Mar 06 '20 at 15:21

lioness99a

answered Mar 06 '20 at 15:10

Siong Thye Goh

1 Answers1