Given below are two statements: Statement I: 8 megabytes = 213 gigabytes…
2022
Given below are two statements:
Statement I: 8 megabytes = 213 gigabytes
Statement II: The decimal equivalent of the binary number (11101.101)2 is (29.625)10.
In the light of the above statements, choose the correct answer from the options given below:
Answer: D. Statement I is false but Statement II is true — ConceptDigital storage units scale by powers of two in the binary convention: 1 gigabyte equals 1024 megabytes. Therefore, converting megabytes to gigabytes…
- 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 12 students.
Show answer & explanation
Correct answer: D
Concept
Digital storage units scale by powers of two in the binary convention: 1 gigabyte equals 1024 megabytes. Therefore, converting megabytes to gigabytes requires division by 1024.
A positional binary number is converted by multiplying each bit by its place value. Integer places use non-negative powers of 2, while fractional places use negative powers of 2.
Application
For Statement I, 8 MB = 8/1024 GB = 1/128 GB = 2-7 GB. This differs from 213 GB, so Statement I is false.
For Statement II, (11101.101)2 = 1×24 + 1×23 + 1×22 + 0×21 + 1×20 + 1×2-1 + 0×2-2 + 1×2-3.
The sum is 16 + 8 + 4 + 0 + 1 + 0.5 + 0 + 0.125 = 29.625. Thus Statement II is true.
Cross-check
Multiplying 2-7 GB by 1024 MB/GB returns 8 MB, and converting 29.625 back to binary gives 11101.101. Both checks confirm the calculations.
Result
Therefore, Statement I is false but Statement II is true.