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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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