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:(25) in base 16 equals (00100101) in base 2.
Statement II:(00011011) in base 2 equals (1B) 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 correct because hex 25 splits into 0010 and 0101, giving the binary 00100101.
Statement 2 is correct since binary 00011011 groups into 0001 and 1011, giving hex 1B.
Each hexadecimal digit maps exactly onto a group of four binary bits.
The conversions are simply the reverse of each other and both hold true.
Grouping bits in fours makes hex a compact way to write binary.
The hex digit B stands for the decimal value eleven, which is 1011 in binary.
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