# Question 1 (Decimal and Base 2 Number System)

Question 1: Convert 15 into an equivalent number with base 2.

a) ​$$(11111)_2$$​                     b) ​$$(12111)_2$$​                  c) ​$$(11121)_2$$​                 d) ​$$(111111)_2$$

Solution:

We should remember that numbers system with base 2 is also called binary number system.

To convert number 15 (decimal number system) to a base number system with base 2  we divide it continuously with 2 till the dividend becomes less than 2 – as shown in the table below;

Then we put remainders in a bracket in the arrow wise direction and write ​$$(11111)_2$$

So decimal number 15 is equivalent to ​$$(11111)_2$$​ in base system with base 2

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