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

Statement I:(11001000) in base 2 equals (C8) in base 16 equals (200) in base 10.

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

Statement 1 is true, as (11001000) in base 2 equals 200, which is C8 in base 16 and 200 in base 10.

The binary 11001000 sums to 128+64+8 = 200.

In hexadecimal, C is 12, so C8 is 12 times 16 plus 8 = 200 as well.

Statement 2 is true, as (123) in base 10 equals 01111011 in binary and 7B in base 16.

Here 64+32+16+8+2+1 = 123, and 7 times 16 plus 11 = 123 too.

Four binary digits map neatly to one hexadecimal digit.

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