Which of the following statements is true about the number system?

AThe binary equivalent of decimal 57.625 is 111000.101

B(145) base 6 = (75) base 10

C(1011) base 2 + (1001) base 2 = (20) base 10 ✓ Correct

D(65) base 10 = (220) base 5

Correct answer: (C) (1011) base 2 + (1001) base 2 = (20) base 10

Explanation

In binary, (1011) is 11 and (1001) is 9, and their sum of 20 matches (20) in the decimal system.

The binary of decimal 57.625 is 111001.101, not 111000.101, since 57 is 111001.

(145) in base 6 equals 65 in decimal, not 75.

(65) in decimal equals (230) in base 5, not (220).

Base conversion multiplies each digit by its base raised to the digit's place value.

The binary fraction .101 equals one half plus one eighth, which is 0.625.

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