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
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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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