With reference to different number systems, which of the following statements is true?

A(109) base 10 = (1101001) base 2

B(123) base 5 = (212) base 4 ✓ Correct

C(101) base 16 + (110) base 8 = (429) base 10

D(241) base 6 = (131) base 8

Correct answer: (B) (123) base 5 = (212) base 4

Explanation

(123) in base 5 equals 38 in decimal, and (212) in base 4 also equals 38, making the two equal.

(109) in decimal is (1101101) in binary, not (1101001), which equals only 105.

(101) in base 16 is 257 and (110) in base 8 is 72, summing to 329, not 429.

(241) in base 6 is 97 while (131) in base 8 is 89, so they are not equal.

Comparing number systems requires converting each to a common base such as decimal.

(123) in base 5 is 1 times 25 plus 2 times 5 plus 3, which is 38.

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