To represent the 5 children as a computer bit, we make use of the equation [tex]2^b = n[/tex]. 3 bits are required to represent the 5 children.
Given that
[tex]n = 5[/tex] ---- number of children
The number of bits (b) is calculated as:
[tex]2^b = n[/tex]
Substitute 5 for n
[tex]2^b = 5[/tex]
Take logarithm of both sides
[tex]\log(2)^b = \log(5)[/tex]
Apply law of logarithm
[tex]b \times \log(2) = \log(5)[/tex]
Make b the subject
[tex]b = \frac{\log(5)}{\log(2)}[/tex]
[tex]b = 2.32[/tex]
The number of bits must be an integer. So, we use the greatest integer closest to 2.32. The integer is 3
So:
[tex]b=3[/tex]
Hence, the number of bits to represent the 5 children is 3.
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