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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:
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 digitsSo, 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 €œon€ bit and a 0 represents an €œoff€ 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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