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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 Peta Byte is equal to 250 bits. In the light of the above statements, choose the correct answer from the options given below:

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 Peta Byte is equal to 250 bits. In the light of the above statements, choose the correct answer from the options given below: Correct Answer Statement I is correct but Statement II is false

Statement I: Minimum number of bits required to store any 3-digit decimal number is 10. 

Explanation:

  • To calculate the number of possibilities given the number of digits: possibilities = basen digits
  • So, if you have 3 digits in decimal (base 10) you have 103 = 1000 possibilities.
  • Then you have to find a number of digits in binary (bits, base 2) so that the number of possibilities is at least 1000, which in this case is 210 = 1024 (9 digits isn't enough because 29 = 512 which is less than 1000).
  • If you generalize this, you have: 2n bits = possibilities <=> n bits = log2(possibilities)
  • Which applied gives: log2(1000) = 9.97 and since the number of bits has to be an integer, you have to round it up to 10.

Thus, the statement I is correct.

Statement II: The data in a digital computer is stored in terms of bits/ bytes where one PetaByte is equal to 250 bits.

Explanation: 

  • A collection of 8 bits is called a byte and (on the majority of computers today) a collection of 4 bytes, or 32 bits, is called a word.
  • Any data stored on a computer is just a large collection of bits. 
  • A piece of computer memory can be represented by a series of 0's and 1's, with one digit for each bit of memory.
  • The value 1 represents an “on” bit and a 0 represents an “off” bit.
  • This notation is described as a binary form.
  • A Pb is the unit symbol for the 'Petabyte' and, the short form of Petabyte is Pbyte.  
  • 1 Petabyte = 1024 TB = 250 Bytes = 253 Bits.

Thus, statement II is incorrect.

Therefore, Statement I is correct but Statement II is false

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