Given below are two statements: Statement I: (11001000)2 = (C8)16 = (200)10…
2023
Given below are two statements:
Statement I: (11001000)2 = (C8)16 = (200)10
Statement II: (123)10 = (01111011)2 = (7B)16
In the light of the above statements, choose the correct answer from the options given below:
Answer: A. Both Statement I and Statement II are true. — ConceptA positional numeral’s value is the sum of each digit multiplied by a power of its base. Binary positions use powers of 2; hexadecimal positions use…
- A.
Both Statement I and Statement II are true.
- B.
Both Statement I and Statement II are false.
- C.
Statement I is true but Statement II is false.
- D.
Statement I is false but Statement II is true.
Attempted by 10 students.
Show answer & explanation
Correct answer: A
Concept
A positional numeral’s value is the sum of each digit multiplied by a power of its base. Binary positions use powers of 2; hexadecimal positions use powers of 16, with A = 10, B = 11, and C = 12.
Application
Statement I: 110010002 = 1×128 + 1×64 + 1×8 = 20010. Also, C816 = 12×16 + 8 = 20010. Thus, all three representations denote 200.
Statement II: 011110112 = 64 + 32 + 16 + 8 + 2 + 1 = 12310. Also, 7B16 = 7×16 + 11 = 12310. Thus, all three representations denote 123.
Cross-check
Grouping each binary numeral into four-bit blocks gives 1100 1000 = C8 and 0111 1011 = 7B, independently confirming both equality chains.
Result
Therefore, both Statement I and Statement II are true.