Question

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.

Accepted Answer

C. Converting to base 10: $2061_B = 2B^3 + 6B + 1$ $601_B = 6B^2 + 1$ Sum = $2B^3 + 6B^2 + 6B + 2 = 432 \implies 2B^3 + 6B^2 + 6B - 430 = 0 \implies B^3 + 3B^2 + 3B - 215 = 0$. $(B+1)^3 - 1 - 215 = 0 \implies (B+1)^3 = 216 \implies B+1 = 6 \implies B = 5$. $1010_5$ in decimal system = $1 \cdot 5^3 + 0 \cdot 5^2 + 1 \cdot 5^1 + 0 = 125 + 5 = 130$.

Number Base System: Sum of Numbers

Explanation

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