# In the binary number system which is used in computer operations, there are only two digits allowed: 0 and 1. How many different binary numbers can be formed using at most four binary digits?

##### 1 Answer

May 15, 2018

#### Explanation:

The total number is the sum of all possible numbers with one, two, three or four digits.

There are exactly

#2^1 = 2# numbers with one digit (#0# and#1# )#2^2 = 4# numbers with two digits (#00# ,#01# ,#10# ,#11# )#2^3 = 8# numbers with three digits (#000# ,#001# ,#010# ,#011# ,#100# ,#101# ,#110# ,#111# )#2^4 = 16# numbers with three digits (#0000# ,#0001# ,#0010# ,#0011# ,#0100# ,#0101# ,#0110# ,#0111# ,#1000# ,#1001# ,#1010# ,#1011# ,#1100# ,#1101# ,#1110# ,#1111# )

So, you have