Given below are two statements with reference to different number systems:…
2023
Given below are two statements with reference to different number systems:
Statement I: (D6C1)16 = (54977)10
Statement II: (41819)10 = (A35B)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 — ConceptIn a positional numeral system with base b, each digit is multiplied by the corresponding power of b, counted from the right starting at power 0. In…
- 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 4 students.
Show answer & explanation
Correct answer: A
Concept
In a positional numeral system with base b, each digit is multiplied by the corresponding power of b, counted from the right starting at power 0.
In hexadecimal, A = 10, B = 11, C = 12 and D = 13. Therefore a hexadecimal number is converted to decimal by expanding it in powers of 16.
Application
Expand (D6C1)16: 13 × 163 + 6 × 162 + 12 × 16 + 1 = 53248 + 1536 + 192 + 1 = 54977.
Expand (A35B)16: 10 × 163 + 3 × 162 + 5 × 16 + 11 = 40960 + 768 + 80 + 11 = 41819.
Thus the decimal value stated in Statement I is obtained, and the decimal value stated in Statement II is also obtained.
Cross-check
Repeated division of 41819 by 16 gives remainders 11, 5, 3 and 10; reading them in reverse and writing 11 as B and 10 as A gives (A35B)16.
Result
Both Statement I and Statement II are true.