Given below are two statements: Statement I: (49)10 = (31)16 = (00110001)2…
2023
Given below are two statements:
Statement I: (49)10 = (31)16 = (00110001)2
Statement II: (7B)16 = (01111011)2 = (123)10
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 — ConceptIn a positional numeral system, a number is evaluated by multiplying each digit by a power of its base and adding the terms. Hexadecimal uses base 16,…
- 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 5 students.
Show answer & explanation
Correct answer: A
Concept
In a positional numeral system, a number is evaluated by multiplying each digit by a power of its base and adding the terms.
Hexadecimal uses base 16, with B representing decimal 11; binary uses base 2. Leading zeroes do not change a number’s value.
Application
For Statement I, (31)16 = 3 × 16 + 1 = 49. Also, (00110001)2 = 32 + 16 + 1 = 49. Thus all three forms in Statement I represent the same value.
For Statement II, (7B)16 = 7 × 16 + 11 = 123. Also, (01111011)2 = 64 + 32 + 16 + 8 + 2 + 1 = 123. Thus all three forms in Statement II represent the same value.
Cross-check
Converting 49 back gives 3 remainder 1 on division by 16, hence (31)16; and 49 = 32 + 16 + 1, hence (00110001)2.
Converting 123 back gives 7 remainder 11 on division by 16, hence (7B)16; and 123 = 64 + 32 + 16 + 8 + 2 + 1, hence (01111011)2.
Result
Both Statement I and Statement II are true.