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Sagot :
A very simple way to know the number of possible combinations in a binary number is given by the next formula:
[tex]2^n=2^{16}=65536^{}[/tex]Now, we should remember that an hexadecimal number contain 16 different digits, from 0 to F. Therefore
[tex]\begin{gathered} 16^n=65536 \\ n\ln 16=\ln 65536 \\ n=\frac{\ln 65536}{\ln 16} \\ n=4 \\ 16^4=65536 \end{gathered}[/tex]Thus, we will need 4 hexadecimal numbers to achieve the same values as a 16-bit number.
For the base-5 number we can do a similar procedure:
[tex]\begin{gathered} 5^m=65536 \\ m\ln 5=\ln 65536 \\ m=\frac{\ln 65536}{\ln 5} \\ m=6.89\approx7 \\ 5^7^{}=78125 \end{gathered}[/tex]Therefore, we would need at least 7 numbers base-5 to achieve something similar to 16-Bit number
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