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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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