Given below are two statements with reference to number systems. In the light of the above statements, choose the most appropriate answer from the options given below.
Statement I:(499) in base 10 equals (111110011) in base 2.
Statement II:(1011101) in base 2 equals (93) in base 10.
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
Both binary conversions are accurate, confirming the two statements hold true.
Statement 1 checks out because 111110011 in binary sums the place values to 499 in base ten.
The set bits 256, 128, 64, 32, 16, 2, and 1 together give exactly 499.
Statement 2 checks out because 1011101 in binary adds 64, 16, 8, 4, and 1 to make 93.
Each binary digit carries a power of two, doubling from right to left.
Converting binary to decimal simply sums the powers of two where a 1 appears.
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