# Question 7 ( Conversion from binary system to decimal system)

Question 7: Convert ​$$(1101)_2$$​ into equivalent number in decimal system.

a) 12                   b) 13                       c) 14                    d) 11

Solution:

Since here the base is 2 – and  digits in the number are 4 i-e 110 and 1- so there will be 4 powers of the base i-e 3,2,1 and 0 !

we multiply first digit 1 with highest powered base i-e ​$$2^3$$​, second digit 1 with next highest powered base i-e with ​$$2^2$$​, next digit 0 with next highest powered base i-e ​$$2^1$$​ and the last digit 1 with least and the last powered base i-e ​$$2^0$$​.

Mathematically,

$(1101)_2= 1\times2^3+1\times 2^2 + 0 \times 2^1 + 1\times 2^0$

It becomes,

$(1101)_2= 8+4+0+1$

So,

$(1101)_2=13$

i- given number in binary system (i-e base 2 system) is equivalent to 13 in decimal (ordinary) system.

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