Given below are two statements: Statement I: Minimum number of bits required…
2020
Given below are two statements:
Statement I: Minimum number of bits required to store any 3-digit decimal number is 10.
Statement II: The data in a digital computer is stored in terms of bits/ bytes where one PetaByte is equal to 250 bits.
Choose the correct answer from the options given below:
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is correct but Statement II is false
- D.
Statement I is incorrect but Statement II is true
Attempted by 24 students.
Show answer & explanation
Correct answer: C
Concept
To store a value in binary you need enough bits to give each possible value a distinct pattern: n bits produce 2n patterns, so storing values up to a maximum M needs the smallest n with 2n > M. Separately, the storage-unit ladder is byte-based: 1 byte = 8 bits, and 1 PetaByte = 250 bytes (strictly a pebibyte, since standards bodies reserve “petabyte” for a decimal quantity, but this question follows the common exam convention treating the two as equal), so a PetaByte equals 250 x 8 = 253 bits, not 250 bits.
Applying it to each statement
Statement I — the bit count. A 3-digit decimal number runs up to 999. Since 29 = 512 covers only 0-511 and 210 = 1024 covers 0-1023, the value 999 fits in 10 bits but not in 9. So the minimum is 10 bits — Statement I is true.
Statement II — the unit. One PetaByte is 250 bytes. Converting to bits multiplies by 8: 250 x 23 = 253 bits. Equating one PetaByte with 250 bits drops the byte-to-bit factor of 8, so Statement II is false.
Cross-check
Statement I true and Statement II false together point to: “Statement I is correct but Statement II is false.” As a sanity check, 999 in binary is 1111100111 — exactly 10 binary digits — and 250 bits would be only one-eighth of a PetaByte (an eighth of 1 PB = 128 TB), confirming the unit in Statement II is wrong.