Question 23

In a number system the product of 44$$_{10}$$ and 11$$_{10}$$ is 3414. The number 3111 of this system, when converted to the decimal number system, becomes

Solution

The product of 44 and 11 in decimal is 484.
If base is x , then 3*x^3+4*x^2+x+4 = 484 .
Hence, the given base system is of number 5.
Now, we have to convert 3111 (in base 5) to decimal number system.

3111 in base 5 equals $$1*5^0 + 1*5^1 + 1*5^2 + 3*5^3 = 1+5+25+375=406$$

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In a number system the product of 44$$_{10}$$ and 11$$_{10}$$ is 3414. The number 3111 of this system, when converted to the decimal number system, becomes

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