Paper 1 · ICT
UGC NET June 2023 (13.06.2023) Shift-I
Given below are two statements. Statement I: (1011101) in base 2 equals (135) in base 8. Statement II: (71) in base 8 equals (111001) in base 2. In the light of the above statements, choose the correct answer from the options given below.
- Statement I: (1011101) in base 2 equals (135) in base 8.
- Statement II: (71) in base 8 equals (111001) in base 2.
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 — Both statements are true, so the answer is that both Statement I and Statement II are true.
Explanation
★Both statements are true, so the answer is that both Statement I and Statement II are true.
★To convert binary to octal, group the bits in threes from the right: 1011101 becomes 001, 011, 101.
★Those groups read as 1, 3 and 5, giving the octal number 135, confirming Statement I.
★For Statement II, each octal digit expands to three bits: 7 becomes 111 and 1 becomes 001.
★So 71 in octal becomes 111001 in binary, confirming Statement II.
★The base of a number system is the count of distinct digits it uses: binary uses 2, octal uses 8.
★The three-bit grouping works because 8 equals 2 cubed, so each octal digit maps exactly to three binary digits.
Want more like this? Create a free account to practise a full test, track your progress, and get spaced-repetition review.
Shared by Mcqkart · via Mcqkart.in