Given below are two statements. In the light of the above statements, choose the most appropriate answer from the options given below.
Statement I:(240) in base 10 equals (11110000) in base 2.
Statement II:(101011111101010) in base 2 equals (57EA) in base 16.
ABoth Statement I and Statement II are correct ✓ Correct
BBoth Statement I and Statement II are incorrect
CStatement I is correct but Statement II is incorrect
DStatement I is incorrect but Statement II is correct
Correct answer: (A) Both Statement I and Statement II are correct
Explanation
Statement 1 is accurate because 11110000 in binary sums 128 plus 64 plus 32 plus 16, which equals 240 in decimal.
Statement 2 groups the binary into nibbles 0101, 0111, 1110 and 1010 reading through the string.
Those nibbles convert to 5, 7, E and A, producing 57EA and matching the binary, which makes Statement 2 accurate as well.
Grouping four bits from the right is the standard way to turn binary into hexadecimal.
Decimal conversion instead multiplies each bit by its power-of-two place value.
Both conversions check out, making both statements true.
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