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Given below are two statements:Statement I: The largest decimal number that can be represented using a 7-bit binary number is 128.Statement II: Minimum number of bits required to store largest 2-digit decimal number is 7.In light of the above statements, choose the correct answer from the options given below:
In the digital computer, there are four types of number systems used for representing information i. e-Binary Number System Decimal Number System Hexadecimal Number System, and Octal Number System. The binary number system uses only two digits, either 0 or 1, and the decimal number system contains ten digits from 0 to 9(base 10). Statement I: The largest decimal number that can be represented using a 7-bit binary number is 128. In general, the largest unsigned number with n bits is 2^n-1, with all the bits being 1. For example:For n=5, 32€“1=31For n=6, 64€“1=63For n=7, 128€“1=127Hence, the statement I is incorrect. Statement II: Minimum number of bits required to store the largest 2-digit decimal number is 7. The decimal number system where we use the digits 0 to 9 to represent a number. So the largest 2-digit decimal number is 99How to Convert 99 in Binary?Step 1: Divide 99 by 2. Use the integer quotient obtained in this step as the dividend for the next step. Repeat the process until the quotient becomes 0. Step 2: Write the remainder from bottom to top i. e. in the reverse chronological order. This will give the binary equivalent of 99. Therefore, the binary equivalent of decimal number 99 is 1100011 which is formed by 7 Binary digits. Hence statement II is also correct. Therefore we can conclude that Statement I is false but Statement II is true.
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