Given below are two statements regarding different number systems. In the light of the above statements, choose the correct answer from the options given below.
Statement I:(D6C1) in base 16 equals (54977) in base 10.
Statement II:(41819) in base 10 equals (A35B) in base 16.
ABoth Statement I and Statement II are true ✓ Correct
BBoth Statement I and Statement II are false
CStatement I is true but Statement II is false
DStatement I is false but Statement II is true
Correct answer: (A) Both Statement I and Statement II are true
Explanation
Both conversions are correct, so both statements are true.
Statement 1 is true because hexadecimal D6C1 equals 54977 in decimal.
That follows from weighting each hex digit by powers of sixteen.
Statement 2 is true because decimal 41819 equals A35B in hexadecimal.
Repeated division by sixteen produces the digits A, 3, 5 and B.
Hexadecimal offers a compact way to write large binary values.
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