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in this video we are going to discuss so how to represent a decimal number with minimum number of digits that means so in this video specially we are going to discuss so how many digits are required how many binary digits are required for a specific visit same decimal number so here see the problem how many bits are required to represent a 16 digit decimal number so for example 6 decimal number 16 digits means it's a very big number so 2 digit our decimal number means for example 12 3 digit decimal number means 123 4 digit decimal number means 4,000 so like third 16 is it decimal number being such a long number that is so for that number if you want to represent in binary so any any 16 digit decimal number if you want to represent in binary firstly you need to consider the number of binary digits how many binary digits are required to represent 16 digit decimal number so that we'll discuss here we are having a formula between number of digits and the number so here 2 power n must be greater than your number so this is the formula to identify the number of digital bits that you need to take to represent a decimal number so where n is equal into number of digits number of digits so here this formula will show you how many number of digits how many number of binary digits you need to take for a decimal number for a particular bit decimal number so here what they given is 2 power n must be greater than the number is 16 digit decimal number so 16 digit decimal number so you know that so you know that two-bit decimal number you know that the maximum are two bit decimal number is 99 why aren't taking maximum why I am using maximum is whatever we are going to define that should be for maximum then it will satisfy all minimum values also for example if I am saying only 50 bitty bits are enough to represent a 16 digit decimal number it can't work for maximum 16 digit number what is maximum 16 digit number means 1 0 0 0 0 up to 16 or 15 0 so that is 16-bit digit minimum number what is the maximum 16 digit decimal number means 9 9 9 all 16 nines if you take in that is maximum 16 digit decimal number for example here maximum 6 2 digit number is 99 this you can really write like 2 square 10 square so maximum 3 bit number you are having is 999 so this really you can write thank you the nearest value is 10 2 like that if you are having 4 bit then it's nearly is equal into 10 power 4 10 power 4 like that in the same way so in this equation I am going to replace my 16 is a decimal number as 9 9 9 9 so on 9 9 so all 16 nines I am going to consider here so now this 2 power N is greater than so here 10 power 16 I can take like this I can take 10 both 16 like this now I am going to use log formula as you know that X is equal into for example if you are having like this X is equivalent to 10 power B if you are having like this then to get this B value what you are doing is log X base you are taking log log X base 10 will give you B value in the same way so here also I am going to consider log formula so here I am just taking 16 is equal in two so 16 here 16 is greater than I am taking this log here so here 16 is equal into I am taking law so less than log to power in base 10 you can see so I take in in reverse so 16 less than 16 less than log 10 to power n so now this M I can write like here so 16 is less than n into log to base 10 now to get n value so I'm going to get n value n must be greater than I am taking this side and must be greater than 16 by log to base 10 this log to base 10 value may be nearly point 3 I think so this is equal into n by 16 by nearly point 3 means you are going to get must be greater than fifty three point one five six fifty three point one five six you are going to get so now the number of bits must be greater than fifty three point one five six are the number of bits are must be greater than 53 so to represent sixteen digit maximum decimal number if you taken for maximum decimal number it will definitely works for minimum decimal numbers also the number of bits are enough minimum decimal number also so here the number of bits binary bits required to represent sixteen digit decimal number is must be greater than fifty three point one five six so that number must be enough discrete form that means so here that en may be is equal into 54 so if you take in minimum 54 bits so then you can represent all 16 digit decimal numbers in binary so for example if you take in only 52 bits then you cannot represent this number that's why I take in maximum number so maximum 16 digit number in the decimal part so 54 binary digits ones or zeros are required to represent any 16 visit decimal number so like this way we can conserve we can now solve like this type of problems and we can find how many bits are required to represent any digit decimal number