Question

Maximum number is decimal can be find out by :​

Answer 1

Maximum number of decimal can be find out by the bits number.

• In a binary word, the bits value explains the greatest value of a decimal that can be expressed by the same word.
• The formula to determine the same is - M = 2`n - 1, where M represents greatest decimal value and N represents bits number.
• For example - the greatest decimal number which can be represented by four bits will be 15.
• This will be calculated as - M = 2`n - 1 = 2`4 - 1 = 16 - 1 = 15

Answer 2

maximum number in decimal can be find out by  2ⁿ-1

Explanation:

n = number of bits

Maximum number in Decimal  is 2ⁿ - 1

Example  n = 1

1 bit

Largest number  1    in binary = 1 in decimal  = 2¹ - 1

2 bit

Largest number  11    in binary = 3 in decimal  = 2² - 1

3 bit

Largest number  111    in binary = 7 in decimal  = 2³ - 1

4 bit

Largest number  1111    in binary = 15  in decimal  = 2⁴ - 1

Hence when n bit

1111 n time  in binary = 2ⁿ - 1 in decimal

Total numbers can be represented are 2ⁿ   ( from 0 to  2ⁿ - 1)

maximum number in decimal system can be find out by  2ⁿ - 1

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