Given below are two statements. In the light of the above statements, choose the correct answer from the options given below.

Statement I:(49) in base 10 equals (31) in base 16 equals (00110001) in base 2.

Statement II:(7B) in base 16 equals (01111011) in base 2 equals (123) in base 10.

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

Converting 49 to hexadecimal gives 31, as 49 equals three sixteens plus one.

The same 49 in binary is 00110001, so Statement 1 lines up its decimal, hex and binary forms.

In Statement 2, hexadecimal 7B is seven sixteens plus eleven, which equals 123 in decimal.

That 123 in binary is 01111011, so Statement 2 also ties its three forms together.

Both statements convert one and the same value correctly across the three bases.

Each hexadecimal digit maps to exactly four binary digits, which eases such conversions.

Want more like this? Create a free account to practise a full test, track your progress, and get spaced-repetition review.