Question 58

Two numbers in the base system B are 2061$$_{B}$$ and 601$$_{B}$$. The sum of these two numbers in decimal system is 432. Find the value of 1010$$_B$$ in decimal system.

Solution

Converting numbers in decimal system

=> $$2061_B = 2B^3 + 6B + 1$$

and $$601_B = 6B^2 + 1$$

Acc. to ques, => $$2B^3 + 6B + 1 + 6B^2 + 1 = 432$$

Solving above equation, we get : $$B = 5$$

$$\therefore 1010_5$$ in decimal system = $$1(5)^3 + 1(5) = 130$$

Note :- This question is technically wrong as we cannot have digit 6 in Base 5.

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