Two number in the base system B are 2061B and 601B. The sum of these two numbers in decimal system is 432. Find the value of 1010B in decimal system.
Explanation:
(2061)B = (1 + 6B + 2B3)10
(601)B = (1 + 6B2)10
∴ 2B3 + 6B2 + 6B + 2 = 432
⇒ B3 + 3B2 + 3B + 1 = 216
⇒ (B + 1)3 = 216
⇒ B = 5
∴ 10105 = (1 × 53 + 1 × 5)10 = 13010
Hence, option (c).
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